Thursday, June 6, 2002

Registration and coffee
8:00-8:45 

Welcome and Introduction 
8:45-9:00 

Oral session I 	Drug – Drug Interactions (Chair: Janet Wade)
09:00-09:20	Andreas Freidig Development Of A PBPK Model For Drug-Drug Interaction Of Orally Delivered Drugs Using In-Vitro Data 
09:20-09:40	Christian Laveille Simulations Using A Mechanistic DDI Model : Individual Risk Assessment
09:40-10:00	Marie Gårdmark EU Regulatory View On DDI And Population Analyses

Coffee break, Poster and Software session I
10:00-11:00	Posters in group I are accompanied by their presenter

Oral session II	(Chair: Leon Aarons)
11:00-11:30	Jan Freijer Extrapolation Of Pharmacokinetics And Toxicity From Pre-Clinical Data To Humans
11:30-11:50	Elena Mishina Assessment Of The Contribution Of Components In A Combination Drug Product Using Population PK Modeling
11:50-12:10	Iñaki F. Trocóniz Dealing With Autoinhibition Of Drug Clearance In Early Clinical Product Development 
12:10-12:30	 Vladimir Piotrovsky Drug Efficacy Analysis As An Exercise In Dynamic (Indirect-Response) Population PK-PD Modeling 

Lunch
12:30-14:00

Oral session III 	Data transformation, Parameter transformation (Chair: Lewis Sheiner)
14:00-14:40	Jose Pinheiro: Transformations and Variance Functions in Nonlinear Mixed-Effects Models
14:40-15:00	Pascal Girard: Practice

Tea break, Posters and Software
15:00-16:00

Oral session IV	PK/PD (Chair: Oscar Della Pasqua)
16:00-16:20 	Robert Leary A Unified Parametric/Nonparametric Approach To PK/PD Population Modeling 
16:20-16:40 	Celine Brochot Assessing The Additivity Of The Effects Of Drugs In Mixtures 
16:40-17:00 	 Nick Holford Population Disease Progress Models For The Time Course Of HAMD Score In Depressed Patients Receiving Placebo In Anti-Depressant Clinical Trials 

Planning of future PAGE meetings & organization 
17:00-17:30	

Social Evening 
19:00-24:00

Friday, June 7, 2002

Oral session V	(Chair: Pascal Girard)
09:00-09:20	Stefano Zamuner Estimate The Time Varying Brain Receptor Occupancy In PET Imaging
09:20-09:40	Michael Looby Assessing The Robustness Of Competing Dose Regimens To Incomplete Compliance 
09:40-10:00	Eric Snoeck: Model Evaluation

Coffee break, Poster and Software session II
10:00-11:00	Posters in group II are accompanied by their presenter

Tutorial	(Chair: Ferdie Rombout)
11:00-11:30	Charles Warlow: Subgroup Nonsense. Problems In Interpreting And Considering Covariates In Evaluation

Oral session VI	Special Populations 	 (Chair: Eric Snoeck)
11:30-11:50 	Bruce Green Population Pharmacokinetics And Pharmacodynamics Of Enoxaparin In Obese Patients
11:50-12:10	Oscar Della Pasqua/Eliane Fuseau Optimising Design in Paediatric Regulatory Studies
12:10-12:30	Brigitte Tranchand/Silvy Laporte Design And Practical Problems In Population PK Studies In The Elderly

Lunch
12:30-14:00	

Oral session VII	Study Design (Chair: France Mentré)
14:00-14:20	Stephen Duffull Prospective Assessment Of A D-Optimal Design For A Population Pharmacokinetic Study Of Enoxaparin 
14:20-14:40	Sylvie Retout Optimisation Of Individual And Population Pharmacokinetic Designs Using S-Plus 
14:40-15:00	Billy Amzal Bayesian Optimal Design For The Study Of Butadiene Toxicokinetics

Tea break, Posters and Software
15:00-16:00 		

Oral session VIII	(Chair: Janet Wade)
16:00-16:40	Lewis Sheiner Dealing with Missing data in Longitudinal Studies Through Modeling 

Concluding remarks/preview PAGE 2003
16:40-17:00	

Posters Thursday (group I)

Michel Tod Handling Concentrations Below Quantification Limit In Population
Sandrine Micallef Modelling Of Intra-Individual And Inter-Individual Variability In 1,3-Butadiene Metabolism
Liping Zhang Simultaneous Vs. Sequential Estimation In PK/PD Data Analysis
Sophie Gisbert Incorporating Uncertainty And Variability In The Physiological Parameters Of A PBPK Model
Ivelina Gueorguieva Reducing PBPK Models Using Global Sensitivity Analysis And Benefit/Cost Criterion
Chanu Pascal Population Pharmacokinetics Of Epirubicin And Its Main Metabolite Epirubicinol Using NONMEM
Sylvie Saivin Cefepime Monitoring In ICU Patients Using A Population Pharmacokinetic Approach
Kim Emil Andersen A Bayesian Approach To Bergman's Minimal Model
Ulrika Wählby Handling Of Time-Varying Covariates In Population Model Building.
Susanne Bøttcher Bayesian Networks Used In PK/PD Modelling
Sylvie Saivin Validation Of An Amikacin Population Pharmacokinetics Model To Be Used In Intensive Care Unit
René Bruno Assessment Of The Predictive Performance Of A New Population Pharmacokinetic Model For Trastuzumab (Herceptin) And Simulation Of Trastuzumab Steady-State Exposure During Long-Term Weekly Dosing.
Andreas Groth Discussion Of Criteria For Evaluating The Quality Of Glucose Clamp Studies
María José García Sánchez Population Pharmacokinetics Of Long-Term Methotrexate In Children With Lymphoblastic Leukemia
María José García Sánchez Phenytoin Covariate Models For Michaelis-Menten Pharmacokinetics In Adult Epileptic Patients
Chantal Csajka Population Pharmacokinetics And Effects Of Efavirenz In Hiv Patients
Jakob Ribbing The Effect Of Collinearity On The Selection Of Covariates In Population Pharmacokinetic Analysis
Hussain Mulla Population Pharmacokinetics Of Theophylline During Paediatric Extracorporeal Membrane Oxygenation (ECMO) 
Marta Valle Pharmacokinetics Of The Three Main Alkaloids Present In The South American Psychoactive Beverage Ayahuasca After Oral Administration To Healthy Volunteers
Siv Jonsson Estimating Bias In Parameters For Some NONMEM Models For Ordered Categorical Data

Posters Friday (group II)

Juan Jose Perez Ruixo Population Pharmacokinetic Analysis Of Zarnestra Using Data From Phase I Clinical Trials
Jean-Baptiste Fau Population PK/PD Modelling Of A New Mao-B Inhibitor In Young And Elderly Healthy Volunteers.
Valerie Cosson Efficiency Of Using Population Pharmacokinetics To Demonstrate Bioequivalence With Sparse Sampling In Cancer Patients-  A Trial Simulation With Etoposide
An Vermeulen Modelling Of The Effect Of Carbamazepine On The Pharmacokinetics Of Risperidone In Psychotic Patients Of Different Phenotypes
Yann Merle Nonparametric Population Analysis Of Amikacin Pharmacokinetic Data In A Pediatric Population.
Laurent Claret The Use Of A Stochastic Model For Data Exhibiting Heterogeneous Pharmacokinetics
Laurent Nguyen Population Pharmacokinetics Of Vinflunine From Phase I Data And Evaluation Of Population Sampling Designs For Further Clinical Development
Xuejun Chen Population PK Modeling Of Drugs Exhibiting Less Than Proportional Increases In Pharmacokinetics Relative To Increasing Doses
Amy Yao Population Pharmacokinetics Of Cyclophosphamide And Its Metabolites In Hematopoietic Stem-Cell Transplantation Patients
Athanassios Iliadis Information Indexes For Exploratory Data Analysis In Population Pharmacokinetics
Sophie Glatt Pooled PK Analysis Of Interferon-Beta-1a (Rebif), Data Obtained In Healthy Subjects And In Patients.
Lars Lindbom Symmetry And Coverage Of Confidence Intervals For A Population PK Model.
Ziad Hussein Retrospective Population Pharmacokinetics Of Cetirizine In Infants And Children
Xiaofeng Wang Population Pharmacokinetics Model Validation Using Kinetica
Nathalie Perdaems The Use Of Physiologically Based Pharmacokinetic (PBPK) Model In Drug Development
Laurence Del Frari Pharmacokinetic Mixed Effects Modelling Of S 16257 After Oral Administration In The Beagle Dog; Combined Analysis
Annabelle Diot Gauss Hermite Quadrature In Population Parameters Estimation. Application To The Detection Of Subpopulations
Hui Kimko Population pharmacokinetic and pharmacodynamic modeling of etanercept using logistic regression analysis
Florence Hourcade-Potelleret Mixture models : simulation and estimation with NONMEM
Judith L. Jacobsen Grey-box Modelling of Insulin Clamp Study
Delphine Martin Pharmacokinetic mixed effects modelling of a new compound in rat - Combined analysis
In-Sun Nam The propagation of information in PK modelling: The use of IV information to support the analysis of PK data 
Gudrun Wuerthwein Population Pharmacokinetics of High-Dose Etoposide in Children Receiving Different Conditioning Regimens

Bayesian Optimal Design for the Study of Butadiene Toxicokinetics

Billy Amzal - Frédéric Bois
ENGREF - INERIS
oral presentation
As a following of the paper 'Optimal design for a study of butadiene toxicokinetics in humans' (Bois and Smith, Toxicol Sci, 1999; 49:213-24), we propose a simulation-based approach to decision theoretic optimal Bayesian design in the context of population pharmacokinetic (PK)models (repeated measurement model, random effects regression models, population models). We investigate the optimal design for the number of subjects and sampling times per subject in a study of 1,3-butadiene toxicokinetics in humans. For that purpose, we maximize, under cost restrictions, a utility function that represent the information provided by the experiments. We implement the MCMC scheme developped by Peter Müller in a recent paper. The Bayesian framework allows us to use data from previous experiments and gives us a robust method to determine a non-sequential and ready-to-use optimal design.

Assessing the Additivity of the Effects of Drugs in Mixtures

CELINE BROCHOT, WILLIAM COUET, ANDREW GELMAN, FREDERIC YVES BOIS
INERIS, Verneuil en Halatte, France
oral presentation
A general statistical model to assess the effects of combinations of any number of drugs is presented. The model is applicable to data collected following an experimental protocol called `direct assay'. In such a protocol, drugs are gradually applied until a target response is observed. At that point in time, some measure of effective (e.g., internal) dose is obtained for each agent. The model, developped in a Bayesian framework, takes inter-individual variability, measurement error and dose- response relationship into account. To check the model, data were simulated using a polynomial dose-response model.Synergism simulated by the data was detected and reasonable estimations were obtained for the parameters. An application to a real data set, on pefloxacin and theophylline mixture-induced seizures in rats, is demonstrated. A previous analysis of these data, using an approximate method, had estimated a negative interaction between these compounds. In contrast, we found the effect of mixtures of these two agents to be approximately additive. We attribute our new finding to an improved treatment of measurement error in our model. Two other data sets, on norfloxacin and theophylline and on norfloxacin and pefloxacin induced seizures in rats, were studied. In these cases, our method confirmed previous analyses.

Assessing the robustness of competing dose regimens to incomplete compliance

Mick Looby
Novartis Pharma AG, Basel, Switzerland
oral presentation
In drug development, non-compliance to the prescribed regimen is the Cinderella of pharmacotherapy. However, instead of being an ignored beauty, its consequences are ugly: poor characterisation of the dose response relationship, improper selection of the optimal dosage regimen and overall increased risk to patients. The clinical pharmacology of interrupted dosing ("pharmacolapsy") is a mostly unwritten book about a frequently recurring event. One of the key decisions in drug development beyond the actual dose strength is the choice of the dose interval. Nowadays it has become almost an imperative to develop drugs that can be taken once daily. One of the reasons commonly touted for this is that patients are more compliant on QD regimens. While there seems to be a relationship between noncompliance and increased frequency of dosing, there is much evidence to support the fact that the impact of QD vs BID dosing with respect noncompliance is minor (approx. 73 vs 70%)[1]. The impact of noncompliance on a particular pharmacotherapy depends on the PK/PD properties of the drug or more precisely the pharmaceutical formulation. Drugs which have long duration of action relative to their dosage interval are more robust to noncompliance. This robustness has been coined forgiveness and is specifically defined as the difference between the drugs post-dose duration of action and the prescribed dosage interval. In order to optimise a therapy the dosing regimen should reflect the forgiveness potential of a formulation so as to minimise the effects of non- compliance. Given the pressure for QD dosing, it is often essential to provide a clear rational for recommendations beyond this mode of administration. Against this background, a method for demonstrating the robustness of competing regimens is presented A naïve model for noncompliance A naïve model of noncompliance tries to capture typical patient compliance behaviour. Several studies have demonstrated that the distribution of overall fraction of doses taken is skewed toward a median in the range of 70-90%, while median compliance with prescribed intervals is in the range of 20-40%. However these figures were subject to large interindividual variability. Urquhart [1] has come up with the following rule of thumb to summarise average noncompliance behaviour: one in six patients: 
•	Remedicates punctually 
•	Takes prescribed doses, but with somewhat erratic timing 
•	Skips an occasional dose, but never more than one 
•	Skips three or more sequential days' doses (a 'drug holiday') 3-4 times per year 
•	Has one or more drug holidays per month  
•	Takes few or no doses, but creates the illusion of good compliance 
This rule provides the basis for assigning types of behaviour to portions of a population. Under the assumption that an individual's pattern of dosing should correspond to a prescribed frequency of dose taking, and assuming that any one dosing event depends only on the occurrence of the previous dosing event, given the individual's probability density function of dosing frequencies, a Markov process can be used to describe the time series of dosing events. A probability is assigned for missing (Pmiss) a dose; if a dose is missed then a probability is assigned for taking (Ptake) the subsequent doses conditional on having missed the previous dose Pmiss controls the frequency at which doses are missed; Ptake controls the duration of drug holidays. The average duration of a drug holiday is given by: 1/Ptake-1. The drug taking behaviour as described above by the rule of sixes can then be roughly characterised by the setting appropriate values for the above probabilities. The timing of dosing can also be appropriately perturbed from the nominal dosing times. This naïve compliance model can then be linked as the input to a population PK (/PD) model for the compound in question. The effect of incomplete compliance can be assessed through simulation by counting the number of days or dosing intervals in which adequate concentrations or target effects are achieved or maintained over the treatment period. The latter can thus be used as an index for the performance of competing regimens in the presence of noncompliance. An anonymous worked example of the model will be presented and possible extensions to the basic model will be discussed. 
[1]Urquhart J. Pharmacodynamics of variable patient compliance: implications for pharmaceutical value. Advanced Drug Delivery Reviews 33 (1998) 207-219. 

Estimate the time varying brain receptor occupancy in PET imaging

Stefano Zamuner, Roberto Gomeni, Alan Bye
GlaxoSmithKline
oral presentation
Positron-Emission Tomography (PET) is an imaging technology currently used in drug development as a non-invasive measure of drug distribution and interaction with biochemical target system. The level of receptor occupancy achieved by a compound can be estimated by comparing time-activity measurements in an experiment done using tracer alone with the activity measured when the tracer is given following administration of unlabelled compound. The effective use of this surrogate marker as an enabling tool for drug development requires the definition of a model linking the brain receptor occupancy with the fluctuation of plasma concentrations. However, the predictive performance of such a model is strongly related to the precision on the estimate of receptor occupancy evaluated in PET scans collected at different times following drug treatment. Several methods have been proposed for the analysis and the quantification of the ligand-receptor interactions investigated from PET data. The aim of the present study is to evaluate alternative parameter estimation strategies based on the use of non-linear mixed effect models allowing to account for intra and inter-subject variability on the time-activity and for covariates potentially explaining this variability. A comparison of the different modeling approaches is presented using real data. The results of this comparison indicates that the mixed effect approach with a primary model partitioning the variance in term of Inter- Individual Variability (IIV) and Inter-Occasion Variability (IOV) and a second stage model relating the changes on binding potential to the dose of unlabelled drug is definitely the preferred approach.

ASSESSMENT OF THE CONTRIBUTION OF COMPONENTS IN A COMBINATION DRUG PRODUCT USING POPULATION PK MODELING

Elena Mishina and Mehul Mehta
US FDA
oral presentation
Drug A has a highly variable pharmacokinetics (PK) with a short half-life, nonlinear at high doses, inactivated by metabolism, and influenced by circadian fluctuation. Modulation of its PK aimed half-life prolongation and decrease of metabolism. A new proposed combination drug product BC contains a prodrug of Drug A, Drug B, and an endogenous substance C, potential competitor of A for metabolizing enzyme. 
Purpose: To evaluate the contribution of substance C in the combination BC by applying the population modeling of PK data from the study of combination BC. 
Methods: BC was administered orally as single ascending doses (1-4 units) and chronic daily doses of 3 units. Blood samples were obtained on four occasions: post single dose and on days 8, 15 and 28 after the multiple doses and assayed for A, B, and C. Data were analyzed with NONMEM. 
Results: The model described B and C kinetics independently. The estimated low value of the fraction conversion B to A was consistent with the previously proposed intracellular mechanism of this process. The full model described a competitive inhibition of drug A elimination by the endogenous substance C. The obtained IC50 value correlated with Km values for C in tissues obtained in vitro and indicated that the influence of C on A elimination was marginal. 
Conclusions: This population PK model described a complex system of prodrug, active metabolite, and interaction of the latter with the competitor. It enhanced the FDA's ability to interpret scientific information regarding the contribution of components in combination drug products. In conjunction with medical data, the results of this modeling challenged the claim in the NDA that C contributed to the efficacy of new combination product. 

A Unified Parametric/Nonparametric Approach to PK/PD Population Modeling

R. H. Leary(1), R. Jelliffe(2), A. Schumitzky(2), and M. Van Guilder(2)
(1) UCSD, San Diego, CA and (2) Laboratory for Applied Pharmacokinetics, USC School of Medicine, Los Angeles, CA
oral presentation
Currently the most popular computational methods for PK/PD population modeling are based on a parametric maximum likelihood (ML) approach that assumes normality or lognormality for the underlying population distribution. In order to reduce computational requirements to reasonable levels, these direct parametric methods make approximations in the computation of the likelihood function that significantly compromise statistical consistency. We have often observed, for example, that such methods introduce artificial correlations between population parameters. 
Nonparametric ML methods, such as the NPEM and NPAG programs from our laboratory, have obvious advantages for situations where unimodal parametric distributions may be unrealistic, such as multimodal populations of fast and slow metabolizers. Here it is shown that nonparametric ML methods can also be advantageously applied to the unimodal parametric case to obtain consistent parametric estimators that avoid the difficulties caused by likelihood approximations. 
Nonparametric ML methods produce distribution estimators that can be interpreted as a set of direct observations of the PK/PD parameters for a finite set of virtual subjects, even though there are no such direct observations in the available data. If the nonparametric ML problem is solved exactly, i.e. a global maximum to the likelihood function is found, then the means and covariances of these virtual direct observations are in fact consistent estimators of the means and covariances of an assumed normal or lognormal parametric distribution. 
We have recently combined the use of adaptive grids with a primal-dual interior-point algorithm to obtain such globally optimal nonparametric solutions with no introduced approximations. In many cases this can now be done on a single-processor PC, whereas previous nonparametric methods based on the EM algorithm often required a supercomputer to obtain the necessary accuracy. By the simple extension mentioned above, a computationally efficient and statistically consistent common method for both the parametric and nonparametric PK/PD population problems is obtained.
Examples using both simulated and real data are given to illustrate the method.

Population pharmacokinetics and pharmacodynamics of enoxaparin in obese patients

Bruce Green and Stephen Duffull
School of Pharmacy, University of Queensland, Brisbane, Australia
oral presentation
Background Enoxaparin dosing is currently based on total body weight. It is not known how to dose adjust patients who are overweight or obese. This population PKPD study was undertaken to determine a suitable dosing strategy for such patients.
Methods Ninety six patients were recruited in the study. Patients were stratified according to body mass index such that one third of patients had a body mass index <24.9 kg/m2 (normal weight), one third from 25-29.9 kg/m2 (overweight) and one third >30 kg/m2 (obese). Approximately three blood samples were taken per patient to determine anti Xa concentration. The occurrence of bruising was also recorded.
Results Analysis was undertaken using NONMEM (version 5). A two compartment linear model with additive error was fitted to the data. Population estimates for clearance (CL) and central volume compartment (V2) (± SE) were 0.9 (0.07) L.hr-1 and 3.7(0.87) L respectively. Peripheral volume (V3) was estimated at 12.7 (6.1) L, absorption rate constant (Ka) at 0.181 (0.0411) hr- 1 and the intercompartmental clearance (Q) at 0.356 (0.175) L.hr-1 with between subject variability of Cl and V2 estimated at 41.7% (39) and 67.6% (29) respectively. Post hoc estimates of CL for each patient were correlated with ideal body weight (r2=0.183), lean body weight (r2=0.212) and sex. V2 was correlated with total body weight (r2=0.22), body surface area (r2=0.203) and body mass index (r2=0.197). The covariate analysis showed CL was best described by lean body weight, and V2 by total body weight. The probability of bruising was modelled using logistic regression and was best described by Cmax and age.
Conclusions Current dosing guidelines for enoxaparin are 100IU/Kg - total body weight every twelve hours. Our findings suggest that this dosing strategy is suitable for patients who weigh less than 120Kg, and those above this weight should be dosed at 100IU/Kg - lean body weight every eight hours.

Prospective assessment of a D-optimal design for a population pharmacokinetic study of enoxaparin

Stephen Duffull and Bruce Green
School of Pharmacy, University of Queensland, Brisbane, Australia
oral presentation
Background Recently, methods for computing D- optimal designs for population pharmacokinetic experiments have become available. However there are few publications that have prospectively evaluated the benefits of D-optimal design in population or single-case settings. This study compared a population optimal design with an empirical design for estimating the baseline pharmacokinetic model for enoxaparin in a stratified randomized setting.
Methods The population pharmacokinetic D-optimal design for enoxaparin was estimated using the PFIM function (MATLAB version 6.0.0.88) developed by our group previously. The optimal design was based on a one-compartment model with lognormal between subject variability and proportional residual variability and consisted of a single design (0-30 mins, 1.5-5 hours and 11-12 hours post- dose) for all patients. The empirical design consisted of 9 windows representing the entire dose interval. Each patient was assigned to have one blood sample taken from 3 different windows. Windows for blood sampling times were also provided for the optimal design. Ninety six patients were recruited into the study who were currently receiving enoxaparin therapy. Patients were randomly assigned to either the optimal (n=50) or empirical (n=46) sampling design, stratified for body mass index. The exact times of blood samples and doses were recorded.
Results Analysis was undertaken using NONMEM (version 5). The empirical design supported a one compartment linear model with additive residual error, whilst the optimal design supported a two compartment linear model with additive residual error. The optimal model had the same structural and statistical form as the final baseline model estimated from the full data set. A posterior predictive check was performed where the models arising from the empirical and optimal designs were used to predict into the full data set. This revealed the ‘optimal’ and ‘empirical’ data derived models were similar to the full model in terms of bias and precision. 
Conclusions The optimal design supported a more complex model than the empirical design strategy. Optimal design techniques may be useful in the future even when the optimized design was based on a model that was misspecified in terms of the structural and statistical models. 

Drug Efficacy Analysis as an Exercise in Dynamic (Indirect-Response) Population PK-PD Modeling

Vladimir Piotrovsky
Advanced PK-PD Modeling & Simulation, Global Clinical Pharmacokinetics and Clinical Pharmacology, Johnson & Johnson Pharmaceutical Research & Development, Beerse, Belgium
oral presentation
Conventional biostatistical analysis of clinical efficacy trials is based on end-points and ignors the longitudinal nature and hierarchical structure of data. It is challenged by the problem of missing data, particularly, dropouts. Usually, changes from baseline are subject to analysis, and this results in a reduced power. An alternative approach is suggested based on dynamic (indirect response) models and mixed effects. It is generic in the sense that the same mathematical formalism with only minor modifications can be applied to a variety of efficacy/safety responses, continuous as well as categorical. The core equation relates the rate of change of a response variable (R; e.g., a symptom intensity score) to the rates of amelioration (vA) and deterioration (vD):
         dR/dt = vA – aD
Disease progression and drug/placebo effect can affect both rates. Onset of action and tolerance are other components of the model. The model may include a pharmacokinetic component, if drug concentration data are available. Alternatively, a dose-response version of the model can be developed. 
Two examples will be presented (NONMEM software was used for the analysis). The efficacy of drug A was investigated in a double-blind placebo-controlled Phase III trial with 2 active doses. The response variable was a subjective symptom intensity score which can take any value between 0 (no symptoms) and 10 (highest intensity). This required the model prediction as well as some parameters to be appropriately constrained. There were almost no dropouts in this trial, and also no tolerance was observed. The inference was based on a drug efficacy parameter which was the difference between the overall effect and that produced by placebo. The dose- response model was developed and the significant efficacy of the higher dose was proved.
Four active doses of drug B were compared with placebo in a double-blind placebo-controlled parallel- group Phase III trial. The response variable was a score, which had a wide range, and no constraints for model prediction were needed, however, some parameters had to be constrained. The fraction of dropouts was relatively high and dose-dependent. Also, tolerance was evident in a substantial proportion of patients. Several subgroups were detected and implemented using the mixture modelling technique. The time to last observation (continuous covariate associated with dropouts) was found to affect the overall (placebo+drug) efficacy. The dose-response profile was bell-shaped with the maximum efficacy achieved at the intermediate dose.

Population Disease Progress Models for the Time Course of HAMD Score in Depressed Patients Receiving Placebo in Anti-Depressant Clinical Trials

Nick Holford, Jianguo Li, Lisa Benincosa, Mattias Birath
Division of Pharmacology and Clinical Pharmacology, University of Auckland, New Zealand Pfizer Global Research & Development, Groton CT, USA, University of Uppsala, Sweden
oral presentation
Introduction: The time course of depression in humans is well known to be cyclical with episodes of depression and typically spontaneous remission. Despite the definition of a specific cyclical syndrome, seasonal affective disorder, there is almost no quantitative description of the pattern of depression within an episode and from episode to episode in patients with clinical depression. The largest collections of data in individuals arise in the setting of clinical trials of anti- depressants but these trials are typically short (approx. 6 weeks) and span barely half of a typical episode of depression. We have developed a model to describe multiple episodes of depression and applied it to Hamilton Depression scale (HAMD) observations from placebo treated patients in clinical trials of two different drugs. 
Model: An empirical, linked cosine model has been developed to describe multiple episodes of depression. It is capable of describing cyclical depressive episodes with flexibility both within the episode and across episodes within each individual. An episode starts at the least depressed state e.g. lowest HAMD score. The episode is split into 3 sections; onset, depression, and recovery. Each section is characterized by amplitude and length. Variability between episodes is accounted for by a random effects model for the 6 parameters which describe each episode. Variability between subjects is described by additional random effects on these same parameters. An inverse Bateman function was also used to describe short term changes during a clinical trial. 
Computation: Model building and parameter estimation was performed using NONMEM Version V release 1.1. Estimation used the first order conditional method with 3 significant figures for convergence. The Compaq Visual Fortran compiler version 6.6 was used to compile NONMEM. NM-TRAN codes were expressed in extended format for use with Wings for NONMEM version 301 (http://wfn.sourceforge.net). 
Results: Both inverse Bateman and a limited linked cosine model described the short term HAMD data equally well. The models allowed a description of the rate of recovery and exposed the largely unrecognized onset of the next episode of depression towards the end of the trial observation period. The inverse Bateman model is numerically more stable and may be of more practical use for describing the short term time course of disease progression. Longer observation periods are required to fully characterize the time course of depression over multiple episodes. Both models have the ability to distinguish different drug effects affecting rate and magnitude of treatment response in clinical depression. 

Regulatory aspects of population pharmacokinetic drug interaction studies

Marie Gårdmark
Medical Product Agency, Uppsala, Sweden
oral presentation
Information on drug-drug interactions is generally gathered form conventional Phase I studies in healthy volunteers, but information is also generated from Phase II/III using population pharmacokinetic methods. According to the European guideline for drug interactions the outcome of the latter studies should mainly be used as hypothesis generating and the best use of this approach are probably to identify unsuspected interactions as a screening instrument. Another application is to confirm absence of suspected interactions, perhaps arising from indications in vitro, which then could be reflected in the labelling. It is less likely that the approach is used to prove the absence of interactions that has been detected in in vivo conventional interaction studies. The population approach has not been used as much as the conventional studies to quantify interactions and provide dose recommendations for certain drug combinations. However, since data are obtained in the target population for whom the drug is intended, the relevance of the results is increased. Usually, the primary aim of the clinical trial is not detection of interactions and thus the design might not be optimal from a drug-drug interaction perspective. For a successful use of the population approach it is necessary that there are sufficient number of patients receiving the interacting drug and that the interacting drug is administered within a reasonable time frame in relation to the development drug. Thus, for infrequently administered drugs the population approach are of less value. In some situations it is necessary to group the interacting drugs, unless the data set contains sufficient information about a certain drug combination, and grouping by mechanism of interaction is one possible approach. Generally, the population approach has been used to evaluate the effect of other drugs on the development drug. The types of interaction mechanism studied are mainly interactions with respect to metabolism or in rare cases active transporters e.g. renal transport. Some examples will be given. Provided that care is taken to assure quality in the design, study management and data analysis, population pharmacokinetic studies to evaluate drug-drug interactions can be of great value.

Dealing with Autoinhibition of Drug Clearance in Early Clinical Product Development

Iñaki F. Trocóniz*, Ilonka Zsolt**, María J. Garrido*, Marta Valle**, and Manel J. Barbanoj**
*, Departamento de Farmacia y Tecnología Farmacéutica. Facultad de Farmacia. Universidad de Navarra (Pamplona, Spain) **, Centre d Investigació de Medicaments. Institut de Recerca de l HSCSP. Department de Farmacología i Terapéutica. UAB (Barcelona, Spain)
oral presentation
Complexities related with drug clearance such as drug-drug interactions, autoinhibition/induction, genetic polymorphism, dose-dependency, etc, are major issues that sometimes can result in the stop of the development process. In the current study, a new compound with adequate efficacy, tolerability and pharmacokinetic profiles in the 6-1200 mg dose range after single oral administration, showed a clear decrease in clearance after multiple oral administration of 240, 350 or 500 mg to 24 healthy volunteers randomly distributed in three dose groups. The design was as follows: One week after the first administration, six additional doses were given once dialy, therefore the duration of the study was two weeks and a total of 33 blood samples were obtained in each individual for pharmacokinetic evaluation. In this kind of situation the question regarding the ability of the drug to inhibit completely its own metabolism is a critical issue since in such a case the drug would accumulate indefinitely in the body. This point was addressed by population pharmacokinetic modelling since graphic exploration of raw data showed that after the last dose the steady-state was not achieved. Drug absorption and drug distribution were described with a first order process and a one compartment model, respectively. Autoinhibition in clearance was modelled using a feedback model where the plasma drug concentrations inhibited the turnover rate of the elimination (enzymatic) activity in an EMAX manner. The model finally selected, which was internally and externally validated, gave an estimate of maximum degree of clearance inhibition close to 95 %. The possibility of having a reasonable (practical) dose regimen on the basis of the described pharmacokinetic behaviour was explored by computer simulations using the model selected and its parameter estimates together with pharmacodynamic information obtained from previous phase I studies. It was shown that oral doses of 120 mg given once daily, with the additional support of one extra 120 mg dose during the first two days of treatment, resulted in adequate drug exposure profiles reaching the steady-state one week after the start of the treatment.

Development of a PBPK model for drug-drug interaction of orally delivered drugs using in- vitro data

Freidig A, Onderwater R, Bogaards J, Bouzom F and Jochemsen R.
TNO Food and Nutrition Research, Zeist, The Netherlands; Servier, Paris, France
oral presentation
Early screening systems, like in-vitro preparations of human microsomes can give an indication whether or not a pharmacokinetic interaction between two drugs is possible. These systems are suited to indicate the presence of an interaction, but they score low in predicting the relevance of such an interaction for the clinical situation. The same holds true for screening systems of interactions on intestinal transport. Major factors that should be considered when interpreting in-vitro interaction data are: 1) the pharmacokinetics (Tmax and Cmax) of the inhibitor at the site of inhibition, 2) extrahepatic sites of interaction and 3) definition of the available concentration of substrate and inhibitor in both the in-vitro system and in-vivo, at the site of inhibition. To investigate the relevance of these factors a preliminary physiologically based pharmacokinetic model for oral dosing of CYP3A4 substrates and inhibitors has been constructed. The model includes a detailed description of the GI-tract and the liver and simulates the pharmacokinetics of two compounds. Compound specific parameters are taken from in-vitro measurements, where possible. The model was tested by using in-vitro interaction data of Midazolam and Ketoconazole to forecast the clinical effect of Ketoconazole on Midazolam pharmacokinetics.

Extrapolation of pharmacokinetics and toxicity from pre-clinical data to humans

Jan Freijer, Bart Ploeger, Joost DeJongh & Meindert Danhof
LAP&P consultants BV & LACDR, division of pharmacology, Leiden, the Netherlands
oral presentation
Extrapolation of data from animal studies is required to predict pharmacokinetics and/or toxicity in humans during the development of new pharmaceutical products, as well as for risk assessment of unintentional exposure to toxic agents. In physiologically based pharmacokinetics (PB- PK), the process of animal-to-man extrapolation involves the construction of a relevant animal PB-PK model, followed by adjustment of anatomical, physiological, and/or biochemical parameters that are specific for humans. 
Igari and co-workers published an instructive example of PB-PK model application in pharmacology in 1983, for diazepam. In this case, extrapolation involved the adjustment of parameters for tissue volume and perfusion, intrinsic clearance and plasma protein binding. For compounds with complex pharmacokinetics, mechanism-based extrapolation of pharmacokinetic species differences is required. This has been demonstrated recently for the food constituent glycyrrhizic acid and its metabolite glycyrrhetic acid. Successful rat-to-human extrapolation of the PK for this compound was achieved by taking into account in vitro data for pre-systemic metabolism, as well as by implementing the physiological mechanism for entero- hepatic circulation. The most relevant adjustments made to the human PB-PK model were: gall bladder release, a lower activity of the hepatic uptake protein (cMOAT), and a higher fraction bound to plasma protein. After validation of the extrapolated human PB-PK model, the population PK/PD for glycyrrhizic acid’s effects on the renal cortisol metabolism could be modelled for risk analysis in populations with a high liquorice consumption (Ploeger et al 2000). It was observed that the high (77%) interindividual variability in gastro-intestinal transit rate in the study population was the major pharmacokinetic factor that determines the risk for adverse events due to liquorice intake. 
For pharmaceutical products, clinical pharmacokinetics are usually well established from phase I studies. Quantitative estimates for long-term safety of these products during phase II/III trials can be obtained by combining clinical PK data with the results of pre-clinical PK and toxicity studies. The accuracy of the predicted safety profile will be high if species-specific differences in toxicity are mainly caused by pharmacokinetic differences. In this case, the physiological basis of the pharmacokinetic descriptions can be limited, since the PK in humans is known, and a clinical population PK model can be directly linked to a pre-clinical concentration- response relationship. This approach will be demonstrated for a new chemical entity (NCE) under clinical development. Preclinical study data for this NCE did demonstrate the occurrence of ocular toxicity in dogs exposed to doses of 20 mg/kg day or higher, whereas in rats and monkeys no toxicity was observed after doses up to 2000 mg/kg/day. Based on AUC, a 10-20 fold higher exposure was observed in dogs compared to rats. Additional in vitro and in vivo studies identified the parent compound as responsible for the toxicity. These findings were used to combine the clinical population pharmacokinetics with the PK/PD profile in dogs, in order to estimate the safety profile of the NCE in humans during phase II/III studies. 
References: 
-Y. Igari, Y. Sugiyama, Y. Sawada, T. Iga, and M. Hanano. Prediction of diazepam disposition in the rat and man by a PB-PK model. J. Pharmacokin. Biopharm. 11 (6), 1983. 577-93. 
-B. Ploeger, T. Mensinga, A. Sips, J. Meulenbelt, and J. DeJongh. A human PB-PK model for glycyrrhizic acid, a compound subject to presystemic metabolism and entero-hepatic cycling. Pharm. Res. 17 (12), 2000. 1516-23. 

OPTIMISATION OF INDIVIDUAL AND POPULATION PHARMACOKINETIC DESIGNS USING SPLUS

Sylvie Retout, France Mentré
Dpt de Biostatistiques et d'Epidemiologie, INSERM U436, CHU Bichat, Paris, France
oral presentation
An approach based on the Fisher information matrix for non linear mixed effects models, implemented in a generic Splus function PFIM (Population Fisher Information Matrix), is now available to evaluate the expected standard errors of estimation and to compare directly designs in the context of population PK or PD studies [1-2]. Population designs are defined as a set of elementary designs to be performed in a number of subjects, each one composed of several sampling times. The usefulness of this approach compared to extensive simulations was shown [3]. We now address the problem of designs optimisation using Splus. 
First, we developed an Splus function IFIM (Individual Fisher Information Matrix): this function evaluates and optimises individual designs in nonlinear regression, using either a Simplex algorithm, as in the ADAPT software [4], or ‘nlmin’, a minimisation function of Splus based on the quasi-Newton algorithm. Comparison to the results provided by ADAPT shows the relevance of IFIM either for an homoscedastic or an heteroscedastic variance error model. Second, we extended PFIM for optimisation of population designs. We tested the performance of the Simplex and the ‘nlmin’ function, using the example of a one compartment model, with three parameters: volume, rate constant of absorption and rate constant of elimination. The random effects are modelled exponentially and the variance error model is homoscedastic. Different designs, all with a total number of 180 samples, are optimised: first, a design with the same elementary design with three sampling times, to be repeated in 90 subjects; second, a population design composed of three elementary designs each with two sampling times to be repeated in 30 subjects; third the same previous design including in addition the optimisation of the proportion of subjects to be allocated to each elementary design. For each case, the designs optimised with the Simplex algorithm are similar to those optimised using the ‘nlmin’ function. Relevance of the optimisation is shown by comparison to a grid research computed for this example on the first optimised population design. This study confirms that the inclusion of a Simplex algorithm or of the ‘nlmin’ function in IFIM / PFIM gives new efficient Splus tools to the pharmacologist to optimise individual or population designs. 

[1] Retout S, Duffull S, Mentré F. Development and implementation of the population Fisher information matrix for evaluation of population pharmacokinetics designs. Comput Meth Prog Biomed, 2001, 65:141-51.
[2] http://hermes.biomath.jussieu.fr/pfim.htm
[3] Retout S, Bruno R, Mentré F. Fisher information matrix for non linear mixed- effects models: evaluation and application for optimal design of enoxaparin population pharmacokinetics. Stat Med, 2002, in press.
[4] D’Argenio DZ, Schumitzky A. ADAPT II User’s Guide: Pharmacokinetic / Pharmacodynamic Systems Analysis Software. Biomedical Simulations Resource, Los Angeles, 1997. 

Design and practical problems in population PK studies in the elderly

Brigitte Tranchand1, Silvy Laporte2
1 Pharmacokinetic Dpt, Centre Léon Bérard, Lyon, France ; 2 Clinical Pharmacology Dpt, University Hospital Saint-Etienne, France
oral presentation
Ageing is a highly complex and variable process, and old people do not age in a uniform way. Several parameters have to be taken into account before defining the age of the subject, as the chronological age or the biological age. Indeed, ageing is associated with multi-dimensional changes, such as alterations of physiological functions, comorbidities and poly-medications. This may result in modifications of the absorption, distribution, metabolism and excretion of the drugs. Therefore, the information obtained from "young" adults cannot be extrapolated to older patients. 
Studies specific to the elderly must be performed in order to establish strategies for treating elderly patients on a scientific basis. As in adults, PK-PD studies are to be performed in healthy volunteers and/or in patients. PK studies in healthy elderly volunteers are often limited by recruitment problems: no existing national database, no financial interest... How can healthy elderly volunteers be found? What is meant by "healthy"? Are they old? 
PK studies in patients will be discussed:
•	Firstly, studies including elderly patients in prospective phase II or phase III trials in adults; these rule out the problem of the number of samples (population approach), but raise the problem of finding the expected target population. 
•	Secondly, studies including elderly patients in clinical routine practice; they raise the same problems as all other studies performed in clinical practice setting, i.e. make the medical team aware of the necessity of recording actual dosing and sampling times. 
•	Then, studies specifically designed for elderly patients meet the problem of overusing the venous capital for daily nursing and, consequently, of finding enough blood and veins, even for sparse sampling designs. 
•	Lastly, the particular case of anticancer agents, i.e studies specifically designed for geriatric oncology. Due to the lack of information on anticancer drugs in patients over 65, only intuitive dose reductions are used, which may significantly compromise the disease outcome. Using sparse sampling design, with adequate evaluation of the covariates (physiological ones and geriatric evaluation), we could expect to implement facilities for proposing optimal dosing and monitoring protocols for individual elderly patients in order to achieve targeted drug exposure.
In conclusion, the main difficulty is the lack of scientific references on optimal treatment-dosing in the elderly, as well as the lack of socio-economic data available in this population. Therefore, it is necessary to set up, and validate a referential in order to improve monitoring and therapy in elderly patients. This should help improve the quality of therapies and the management of the costs (direct and indirect) induced in this particular population. The best way is to undertake specific studies in the elderly.

Dealing With Missing Data Through Random Effects Models

Lewis SHEINER, MD.
University of California San Francisco, USA
oral presentation
A standard clinical trial assigns treatments A, observes outcomes Y, and, generically, uses the disparity between the goodness of fit of pY(Y|A) vs. pY(Y) to determine if assignment is causal for differences in outcomes. Covariates X may be used with pY(Y|A,X) to sharpen conclusions, but they are not required. With clinical trials of chronic conditions it is almost inevitable that departures from protocol occur. Missingness, wherein one or more scheduled observations in a longitudinal series (i.e., Y is a time-indexed vector with elements Yt, for t an element of t, the set of observation times) are not made, is a common form of departure. Dropout at time T, wherein Yt, t T, denoted Ymiss, is missing is a particularly simple and illustrative form of missingness. With dropout, the observed outcome is (Yobs,T), not Y, and the required model is therefore pY,T(Yobs,T). The standard approach to dropout is to impute Ymiss using LOCF (last observation carried forward), and analyze the now "complete" data using the analysis procedure originally proposed. Whereas this approach may sometimes suffice for a (conservative) confirmatory analysis, it does not generally lead to unbiased conclusions because the LOCF prediction of Ymiss is rarely unbiased. 
More generally, the data distribution pY,T(Y,T|A) can be factored as pT(T|Y,A)pY(Y|A). The first factor, the model for missingness, is potentially causal, as T now depends on Y, and cannot necessarily be ignored (complete case analysis). If an X exists such that pT(T|A,Y,X)=pT(T|A,X) then Ymiss is ignorable (in the sense that pT(T|A,X) may be ignored with only some slight loss of efficiency if it shares parameters with pY(Y|A,X)) and the complete cases can be validly analyzed using pY(Y|A,X) instead of pY(Y|A). 
Failing a covariate that renders the missingness ignorable, heuristically, if Yobs can be used to model E(Ymiss|Yobs), then imputing Ymiss = E(Ymiss|Yobs) makes the missing data be only the residuals, Ymiss - E(Ymiss|Yobs), and these may be almost ignorable (i.e., E(Ymiss|Yobs) may be almost unbiased for Ymiss). LOCF rarely accomplishes this as it recognizes no data trends that might be expected to persist after dropout. Random effects models for the time-evolution of Y can accomplish this: such models assert that pT(T|Y,A)pY(Y|A) = pT(T|b,A)pY(Y|b,A), where the b are random effects. If so, Ymiss no longer affects pT(T|A), and if Yobs supplies unbiased information about b, the missingness is ignorable. Further, such models usually also assert conditional independence of the elements of Y given b, whence pY(Y|b,A) equals the product of the terms pY(Yt|b,A) for all t in t, and the likelihood pY(Yobs|b,A) is immediate.
For a random-effects model-based approach to non-ignorable missingness to be credible, the assumption that given the particular choice of pY(Yt|b,A), Yobs supplies unbiased information about b (which pY(Yt|b,A,tT) = LOCF rarely does) must hold, and this in turn requires that it be scientific (i.e. be based on prior knowledge) as the current data (absent Ymiss) cannot provide evidence for or against it. 

Simulations using a mechanistic DDI model: individual risk assessment.

Christian LAVEILLE, PharmD.1, Lewis SHEINER, MD.2, Vincent DUVAL, PharmD.1, Guillemette RESPLANDY, PhD.1, and Roeline JOCHEMSEN, PhD.1.
(1)Institut de Recherches Internationales Servier, Courbevoie, France; (2)University of California San Francisco, USA
oral presentation
S 16257 is a selective heart rate reducing agent which is developed for the treatment of stable angina pectoris. It is extensively metabolized by a single enzyme, cytochrome P450 3A4 (CYP 3A4), resulting in the formation of an active metabolite, S 18982, also metabolized by the CYP 3A4. Using pharmacokinetic studies in healthy volunteers, a population mechanistic drug-drug interaction (DDI) model was built, derived from Piotrovskij and Van Peer (Pharm Res, 1997). During these phase I studies the parent drug (S 16257) or the active metabolite (S 18982) were administrated by intravenous or oral route, without and with co-administration of substrates and/or inhibitors of the CYP 3A4 (grapefruit juice, verapamil, ketoconazole and josamycin) and all available concentrations (plasma and urine) were used to characterize this population DDI model.
Concurrently, heart rate was measured at rest and during bicycle exercise tolerance tests (ETT). The starting workload was usually 50 Watts and then it was increased by 25/50 Watts every 3 minutes for a total duration of 9/12 minutes. A population PK/PD model was defined taking into account both the concentrations of S 16257 and S 18982 as well as all measured heart rates independently of the workload (from 0 (at rest) to 200 Watts).
After qualification of the different models, it is quite straightforward to predict the population response after administration of substrates and/or inhibitors of the CYP 3A4 in combination with S 16257 or S 18982. However in the case of DDI, the risk of reaching higher exposure is possible in some patients. The evaluation of such patients is important since strong CYP 3A4 inhibitors would be considered for co- administration with S 16257.
After definition of a cardiac safety criterion (for example heart rate at rest below 45 bpm) and software implementation, simulations were performed in order to assess the individual risk which could involve a dose adjustment.

Sub-group Nonsense. Problems In Interpreting And Considering Covariates In Evaluation

Charles Warlow
Dept. of Clinical Neurosciences, Western General Hospital, Edinburgh, UK
oral presentation
Sub-group analysis is driven by our desire as doctors to treat individuals as individuals not as groups – in which sorts of people does the treatment work best, or worst? At the same time, the reliability of the results of sub-group analysis dpends on a number of things which are uncomfortable – a priori and not data-driven hypotheses about what should work and what might not, very large sample size of the overall trial and so in each relevant sub-group, and proper analysis to explore the heterogeneity of treatment effects across all sub-groups under consideration. Furthermore, the results of sub-group analysis should not be suppressed, and ideally they should be replicated in a different trial. So having more than one trial running in parallel has a lot to commend it. But even sub-group analysis is not enough, at least not unless the patients are divided not just into the obvious young or old, male or female etc, but also on the basis of overall baseline risk of a poor outcome. After all, even very risky treatments might be worthwhile in patients with a poor prognosis.

Transformations and Variance Functions in Nonlinear Mixed-Effects Models

Jose Pinheiro
Biostatistics, Novartis Pharmaceuticals
oral presentation
Population pharmacokinetics (PK) studies consist of longitudinal concentration measurements in a sample of individuals, with the concentration profiles typically being represented by nonlinear functions of PK parameters and covariates. Nonlinear mixed-effects (NLME) models flexibly describe nonlinear relationships between a response variable and parameters and covariates in correlated, longitudinal data, being the primary modeling tool for fitting and analyzing population PK models.
In its simplest form, NLME models assume additive Gaussian within-subject errors with constant variance and Gaussian random effects. However, when real data are analyzed, departures from these assumptions are frequently observed. Some of the most common departures are non-normality of within-subject errors and/or random effects and non-constant within-subject variance (heteroscedasticity). In classical regression analysis with independent data, non-normality has been typically dealt with by transforming the response (and sometimes also the model, as in the "transform both sides" approach) and heteroscedasticy has been addressed through either data transformation or the use of variance functions (leading to weighted
regression methods).
This talk discusses the use of transformations and variance functions in the context of NLME models, for the purpose of correcting suspected departures from the model assumptions. Transform both sides strategies for NLME models are described and compared to the use of variance functions, in the context of heteroscedastic data. Parameter transformation to allow unconstrained optimization and to address non-normality in the random effects are also discussed. Real and simulated data from population PK models are used to illustrate the methods described.

Model Evaluation

Eric Snoeck
Exprimo
oral presentation
Model evaluation, or the more stronger term, model validation can be defined as the objective assessment of the predictive performance of a model. As the science of model evaluation is evolving, no formal guidance can be given regarding the model evaluation method to be used. There is no "right" or "wrong" model in that a model can be valid for one purpose and not for another. Consequently, any model evaluation procedure should take into account the intended use of the model.
An examination of over thirty published papers where a variety of model evaluation procedures were performed reveals that the most common method is to predict a relevant variable or parameter, using a separate external "validation" data set. Other reported techniques included cross validation and use of the "posterior predictive check".
The presentation to be given will give an overview of the various possible diagnostic tools and model evaluation procedures via several examples, and will highlight their respective advantages and disadvantages, in light of the intended use of the model.

Optimising Design In Paediatric Regulatory Studies

Oscar Della Pasqua(1) and Eliane Fuseau(2) 
 (1)GlaxoSmithKline, Greenford, UK (2)EMF,Aix-en-Provence, France
oral presentation
Most societies define children population by age group and/or by sexual activity. However, these definitions do not support current PKPD understanding of pharmacological response and physiology. Obvious differences exist between adult and children, which are relevant to the treatment of their disease. These may encompass changes in pharmacokinetics, pharmacodynamics, safety and efficacy assessments.
Pharmaceutical companies do not usually assess the dose-response in the children population, but rather rely on empirical practices and off-label extrapolation. Techniques exist which would allow a rational dose selection in children, based on PKPD bridging studies.  Yet, the approach requires the adequate use of children-specific assessment of the disease and treatment.  Regulatory organs have attempted to encourage companies to retain the initiative of paediatric development for their compounds and issued a number of guidance documents over the last 5 years: FDA (1998), ICH E11 (2000), EMEA (draft 2002). These documents have addressed the issue of drug development for paediatric use only and redefined the timing of the paediatric studies relative to the adult studies.
Current guidelines do not address all relevant issues concerning study design and data analysis. In addition to recruitment issues, examples will be presented that illustrate difficulties in dose selection, sampling scheme, pharmacokinetic disposition and differences in delivery systems and absorption. The use of simulation and extrapolation from adult data is not simple and may lead to bias and imprecision.
Population PKPD modelling is a tool to optimise paediatric drug development program and meet regulatory requirements. Implementation of bridging strategy will allow coherent label for paediatric indication.

Handling Concentrations Below Quantification Limit in Population

MICHEL TOD
Hopital Avicenne, Bobigny, France
poster
Three practical strategies for handling concentrations below the quantification limit (BQL) in the context of the estimation of population parameters were compared. The first method (naïve method), consisted in discarding these values from the data. The second method (LBS method) fixed the BQL values to QL/2, while the standard deviation of the residual error model was fixed to QL/4. The third method (reference method), integrated the likelihood of the BQL values from 0 to QL. The performances of these methods were assessed with simulated data and compared to a fourth method (gold standard) which consisted in estimating the parameters assuming all the observations were available. The influences of the population size, the number of samples per subject, the proportion of BQL values and the sampling schedule were determined. In all cases, population parameters were estimated in a Bayesian framework by using WinBUGS, which relies on sampling-based techniques. Results showed that discarding BQL values leads to a poor estimation of the population parameters especially when the amount of information was low and when the proportion of BQL values was high. In contrast, the LBS method, which is very easy to implement in many softwares, worked very well. The reference method worked only slightly better and was close to the gold standard.

Modelling of intra-individual and inter-individual variability in 1,3-butadiene metabolism

Sandrine MICALLEF, Thomas J. SMITH, Frédéric Y. BOIS
INERIS, Verneuil en Halatte, France
poster
While inter-subject variability is accounted for in population statistical models, less attention has been devoted to intra-subject variability. In this study, we evaluated whether the metabolism of a toxic substance (1,3-butadiene) varies between occasions for a given subject. Two hierarchical models were built. The first one dealt with both inter-subject and inter-occasion variability. The second one dealt only with inter-subject variability. Both models imbedded a common physiologically-based pharmacokinetic model. Physiologically-based modeling brings a framework to include mechanistic knowledge about model structure and parameter values. Eleven human volunteers were exposed twice by inhalation to low levels of 1,3-butadiene (2 parts per million during 20 minutes). For each subject, exhaled air concentration was measured at different times. Posterior distributions of metabolic clearance parameters were studied after Bayesian calibration of both models. Bayes factors indicate that the model including intra-individual variability is clearly superior. Using this model, the intra-individual and inter- individual variability geometric SDs of metabolic butadiene rate constant are close to 1.5. The impact of these findings on the classification of subjects as low / medium / high metabolizers (as often done in biomarker or epidemiological studies) is investigated and discussed.

SIMULTANEOUS vs. SEQUENTIAL ESTIMATION IN PK/PD DATA ANALYSIS

Liping Zhang
UCSF, San Francisico, CA
poster
Introduction Rational drug dosing requires knowledge of the dose[– concentration] – effect relationship, which can be obtained by estimating a predictive pharmacokinetic (PK) – pharmacodynamic (PD) model to both concentration and effect observations from a population. The bivariate data can be fit to a model for both responses simultaneously, or sequentially: first estimate the PK model based on PK data alone, and then estimate the PD model conditional on the PK model estimate and the PD data. We compare the performance of a simultaneous method with that of five sequential method variants with respect to computation time and estimation precision. 
Methods Using NONMEM V, PK/PD observations from different numbers of individuals and various study designs are simulated according to a one or two compartment PK model and direct Emax or sigmoid Emax model, with parameters drawn from an appropriate population distribution, and fitted to a 1 compartment PK model and Emax PD model. Performance measures include computation time, fraction of successful analyses, integrated prediction error (interpolation and extrapolation) and, for cases that the simulation and analysis models are identical, precision of PD parameter estimates. 
Results Sequential approaches take less computation time and are more likely to succeed. When the analysis model is the same as the simulation model, a sequential approach that conditions on subject-specific posterior Bayes PK estimates is as precise as the “gold standard” simultaneous method using an approximate maximum likelihood method, and is considerably faster. When the analysis PK model is misspecified, the simultaneous method has greater precision than the best sequential method; when the analysis PD model is misspecified, sequential and simultaneous methods perform similarly. 

INCORPORATING UNCERTAINTY AND VARIABILITY IN THE PHYSIOLOGICAL PARAMETERS OF A PBPK MODEL

S. Gisbert, I. Gueorguieva, G. Graham, L. Aarons
Centre for Applied Pharmacokinetic Research, University of Manchester
poster
Background: PBPK models are used to scale animal PK to man. However, using average parameters, these models only give rise to mean predictions. As well as the mean result it is important to estimate the variability in predicted concentrations that arises from the existing uncertainty and variability in the model parameters [1]. The parameters of a PBPK model can be described as being either drug dependent (fu, Clint and Kpu) or physiological (tissue volumes and flow rates). Although some work has been done on assessing the contribution of the variability of the drug dependant parameters to the PK variability, little work have been done on the contribution of the uncertainty and variability in the physiological parameters. 
Aim: To incorporate uncertainty and variability in physiological parameters taking into account the relationship between tissue volumes and their corresponding flow rates together with constraints for body weight and cardiac output, respectively. 
Methods: We initially developed a PBPK model for diazepam in rats. The uncertainty and variability in tissue volumes was assumed to follow a truncated Dirichlet distribution [2, 3]. The flow rates were then functionally related to the volumes. The model was used to predict the variability in human PK. The PBPK analyses were implemented in MATLAB 6.1. 
Results and discussion: The incorporation of uncertainty and variability in the physiological parameters accounted for the variability seen in the initial distribution phase, which was not described by the drug dependent parameters. 
References: 
[1]: T. Yates. Predicting Physiological Variability and their Interaction through Interspecies Scaling. Centre for Applied Pharmacokinetic Research. University of Manchester, UK. Annual report 2001. 
[2]: D. Farrar, B. Allen, K. Crump and A. Shipp. Evaluation of uncertainty in input parameters to pharmacokinetic models and the resulting uncertainty in output. Toxicology Letters, 49:371-385, 1989. 
[3]: D. Krewski, Y. Wang, S. Bartlett and K. Krishnan. Uncertainty, variability, and sensitivity analysis in physiological pharmacokinetic models. Journal of Biopharmaceutical Statistics, 5(3): 245-271, 1995.

REDUCING PBPK MODELS USING GLOBAL SENSITIVITY ANALYSIS AND BENEFIT/COST CRITERION

I. Gueorguieva, I. Nestorov, M. Rowland

poster
Currently, PBPK models are used mainly in preclinical drug development to predict human PK extrapolated from animal studies. Due to their complexity these models are not used in later development phases. However, if a PBPK model can be formally reduced but still preserve its physiological meaning and the price, i.e. information loss is explicitly stated, this reduced yet still physiological model can be taken further to Phase I and even Phase II and III. Such a continuous flow of information will improve our knowledge and understanding throughout drug development, which will inevitably better our decision making process. A successful and complete PBPK model should account for the parametric variability and uncertainty as well as recognize structural model uncertainty. Although a number of studies address the issue of propagating parametric variability (mainly by Monte Carlo simulations), structural uncertainty has not been extensively investigated. Sensitivity analysis (SA) studies how the variance of the plasma concentration or pharmacological effect can be apportioned qualitatively or quantitatively to different sources of variation. SA is used to increase the confidence in the model and its predictions by providing an understanding how the model responds to any changes, be they parameters or structure. Carrying out SA is a prerequisite to any model building. Global sensitivity analysis (GLS) is a variance-based method, which takes a sampling approach and the variability and uncertainty range assigned to PK parameters reflects our knowledge of them. All the parameters are varied simultaneously and the sensitivity is measured over the entire range of each input parameter. The aim of this study was to find an optimal (smaller dimensionally) physiologically based pharmacokinetic (PBPK) model for diazepam disposition investigating any loss of information using GLS and a benefit/cost criterion. As a result of the carried out investigation the initial concentration variance was preserved in the obtained lumped PBPK model. 

Population pharmacokinetics of epirubicin and its main metabolite epirubicinol using NONMEM

Chanu Pascal, Tranchand Brigitte, Robert Jacques
Centre Léon-Bérard, Lab Pharmacocinétique, Lyon, France
poster
The marked inter- and intrapatient variability of the pharmacokinetics of a number of antineoplastic agents is well known. Moreover, we can presuppose that there is, at some extent, some variability degree of cardiotoxicity and myelosuppression following an epirubicin therapy, and that this variability is in some fashion related to the administered dose of drug. In the present study, we tried to perform modeling of epirubicin, and its main metabolite epirubicinol, by using covariates in order to reduce inter- and intra patient variability. Indeed, it would be useful to predict pharmacokinetic parameters: clearance (Cl) and volume of distribution (Vd) of central compartment in order to individualize dosage regimen with minimal disturbance to the patient.
35 patients with breast cancer, Hodgkin’s disease or sarcoma entered the study (55 courses, 1 to 3 courses per patient). Each course consisted of a 5 min infusion of epirubicin. Blood samples of 5 ml were collected on heparinized tubes at 15 min, 20 min, 30 min, 50 min, 1 h 10 min, 2 h, 4 h, 24 h et 30 h after the start of the infusion. Epirubicin and its metabolite epirubicinol were assayed by HPLC on reverse phase columns with fluorescence detection. 
Covariates collected were body weight (Bw) (range [45;90] kg), Age (range [26;73] years), Sex (M=1, F=2, ratio M/F = 0.37), creatinemia (SCr) (range : [40;119] µmol/l), bilirubinemia (Bili) (range : [2;19] mg/l), type of cancer (Pat) (Hodgkin’s=0 (n=9) sarcoma=1 (n=17), breast=2 (n=9). 
Data analysis were performed using NONMEM version 5 under Visual-NM. For epirubicin, the best model was a three compartment model associated to a mixed error model (ADVAN 11, TRANS 4). 
The objective function decreased from –4344 to –4497 after introduction of covariates. Variability in clearance decreased from 38% to 26% and in volume of distribution from 33% to 22%. Clearance and volume of distribution could be expressed as follows: 
Cl=[41.0 x (1-Pat) x (2-Pat) + 26.4 x Pat x (Pat-1) + 66.3 x Pat x (2-Pat)] x [ 1 – 0.0075 x (Age – 45) ]
Vd= 10.5 x (1 – 0.33 x (Sex-1)) x (1 + 0.0078 x SCr)
Similar study has been carried out for epirubicinol using a two compartment model and first order absorption.
In conclusion, such a population model, could be used to predict pharmacokinetic parameters for patients before epirubicin therapy.

CEFEPIME MONITORING IN ICU PATIENTS USING A POPULATION PHARMACOKINETIC APPROACH

Georges B., Saivin S., Archambaud M., Conil JM., Decun JF., Cougot P., Virenque C., Houin G.

poster
Introduction: Cefepime is used in the treatment of severe infections caused by Gram-negative bacilli. Pharmacokinetic modifications observed in ICU patients may lead to inadequate serum drug concentrations of the drug. The purpose of this study was to determine the influence of some patients' characteristics on the pharmacokinetics of cefepime, using a population-pharmacokinetic approach and leading to an adequate individual dosing strategy. 
Patients and Methods: After ethical committee approval and informed consent, 34 patients were included. They received cefepime as 2g x 2 or 4 g continuously and 8 to 11 blood samples were drawn. Drug concentrations were measured by HPLC with UV detection. Individual clearances were calculated using Kinetica software. The population pharmacokinetic analysis was carried out using NONMEM. A base-line model was constructed, then the influence of demographic and biological variables was studied. 
Results: A two-compartment model associated to a proportional error model was the most suitable. The index of gravity score (IGS) and weight (WT kg) were significantly correlated with total plasma clearance (CL l/h). Hemoglobin levels (HB g/dl) and WT were significantly correlated with the central volume of distribution (V1 l). The final model was: CL = 16.6 - (0.762 IGS) - 0.239 (70 - WT). V1 = 0.173 - 2.73 HB + 0.574 WT. Q (inter-compartmental clearance) = 12.8. V2 (peripheral volume of distribution) = 22.3 l. We validated our model by comparing the observed individual clearances and the NONMEM predicted clearances (R2 = 0.8082). 
Conclusion: Our data were consistent with those previously reported, concerning the significant variability in pharmacokinetics between ICU patients. We showed that IGS score, weight and hemoglobin levels are factors that may influence the standard dosing of cefepime. Our model enabled us to predict cefepime concentrations in new patients. 

A Bayesian Approach to Bergman's Minimal Model

Kim Emil Andersen and Malene Højbjerre
Aalborg University, Denmark
poster
The classical minimal model of glucose disappearance (Bergman et al., 1979) was proposed as a powerful modelling approach to estimating insulin sensitivity and glucose effectiveness during a standard frequently sampled intravenous glucose tolerance test (IVGTT) or a tolbutamide- or insulin-modified IVGTT. The standard frequently sampled IVGTT consists in administering a single intravenous injection of glucose over a small period of time and measuring in plasma the resulting glucose and insulin concentrations. Two mathematical non-linear models are used to model the dynamics of plasma glucose and the kinetics of plasma insulin. Highly computer intensive deterministic iterative numerical algorithms exist for reconstructing the glucose kinetics and thereby obtain estimates for the insulin sensitivity and glucose effectiveness. However, these algorithms are only efficient when a good initial estimate is provided. In this work we present a Bayesian approach to estimating the insulin sensitivity and glucose effectiveness by adopting graphical models as a powerful and flexible modelling framework. We demonstrate how the reconstruction algorithm may be efficiently implemented through the use of Markov chain Monte Carlo methods. 
Bergman, R.N., Ider, Y.Z., Bowden, C.R. and Cobelli, C.:Quantitative Estimation of Insulin Sensitivity, American Journal of Physiology, 236 (1979), E667-77. 

Handling of time-varying covariates in population model building.

Ulrika Wählby(1), Alison H. Thomson(2), Peter A. Milligan(3) and Mats O. Karlsson(1)
(1)Division of Pharmacokinetics and Drug Therapy, Uppsala University, Uppsala, Sweden (2)University of Glasgow, Dept of Medicine & Therapeutics, Western Infirmary, Glasgow, UK (3)Department of Clinical Pharmacokinetics and Pharmacodynamics, Pfizer Global Research and Development, Sandwich, UK
poster
Time-varying covariates contain more, and to some extent different, information than time-constant covariates. As information is linked to the magnitude or the frequency of change it is of value to document these changes, and also to properly account for the variation in population pharmacokinetic (PK) or pharmacodynamic (PD) modelling. Yet, covariate models seldom differentiate between time-constant and time-varying covariates as in (1), even if there are exceptions (e.g. Taright et al. PAGE 1997). Some examples of extended models which apply only to time-varying covariates are given in (2)- (5) below. 
1) Standard covariate model: 
    P = THETA(1) *(1 + THETA(2) *(COV – medianCOV)) *exp(ETA(1)) 
2) Model for separate inter- and intra-subject variation in the covariate relationship: 
    P = THETA(1) *(1 + THETA(2) *(BCOV – medianBCOV) + THETA(3) *DCOV) *exp (ETA(1)) 
where BCOV and DCOV are the baseline and change from baseline covariate values, respectively 
3) Interindividual variability in covariate relation: 
    P = THETA(1) *(1 + THETA(2) *exp(ETA(2)) *(COV – medianCOV)) *exp(ETA(1)) 
4) Model including predicted covariate values (CÔV) from a model for the covariate: 
    P = THETA(1) *(1 + THETA(2) *(CÔV – medianCÔV)) *exp(ETA(1)) 
5) Time-dissociation of covariate influence: 
    P = THETA(1) *(1 + f (THETA, COV, time)) 
In addition to the models above, there is a possibility that the interpretation of the change in a covariate over time is confounded, as it may be affecting drug disposition, or the change could be caused by the drug treatment itself, or the influence is bi-directional (e.g. a nephrotoxic (hepatotoxic) drug producing decreased creatinine clearance (increased liver enzyme levels) as well as a lowered CL). 
In sequential PKPD modelling essentially all these models (apart from (2)) are regularly applied when associating PK (a time-varying covariate) to PD, however, usually not for associating “traditional” covariates (e.g. lab-values) to PK or PD relationships. How additional information in such time-varying covariates may be utilized in some of these models will be illustrated using real data sets. 
Reference: Taright, N., Mentré F. and Mallet A., Non-stationarity of kinetic parameters in multi-occasion designs. Oral presentation PAGE, Glasgow 1997. 

Bayesian Networks used in PK/PD modelling

Susanne Bøttcher and Claus Dethlefsen
Aalborg University, Denmark
poster
A Bayesian network is a graphical model that encodes the joint probability distribution of stochastic variables, which in our case may be continuous and/or discrete. By specifying the dependency structure through a Directed Acyclic Graph (DAG), the joint probablility distribution factorizes according to this DAG. Here we restrict us to Conditional Gaussian (CG) networks. This is to ensure availability of exact local computation methods. The class of models comprise linear models with a complex dependency structure, for example time series models. 
A method for estimating the parameters and learning the dependence structure of networks with mixed variables is presented in Bøttcher (2001). If used on networks with only discrete or continuous variables, it coincides with the methods developed in Heckerman et al. (1995) and Geiger and Heckerman (1994). 
We are developing a package, written in R, which provides methods for analysing datasets using Bayesian networks, see Bøttcher and Dethlefsen (2002). In particular the package includes procedures for defining priors, estimating parameters, calculating network score, performing heuristics search as well as simulating datasets with a given dependency structure. 
We illustrate the methodology by examples from PK/PD studies of drugs for use in the treatment of Type II diabetes. 
Bøttcher (2001), Learning Bayesian Networks with Mixed Variables, Proceedings of the Eighth International Workshop in Artificial Intelligence and Statistics 2001. 
Bøttcher and Dethlefsen (2002), A package for Learning Bayesian Networks, ongoing work. 
Geiger and Heckerman (1994), Learning Gaussian Networks, Technical Report MSR-TR-94-10, Microsoft Research. 
Heckerman, Geiger and Chickering (1995), Learning Bayesian networks: The combination of knowledge and statistical data, Machine Learning. 

VALIDATION OF AN AMIKACIN POPULATION PHARMACOKINETICS MODEL TO BE USED IN INTENSIVE CARE UNIT

RIZO-MANIKA M, SAIVIN S, GEORGES B, CONIL JM, LAVIT M, HOUIN G

poster
Introduction: Amikacin (AMIK) is one of the most useful aminoglycoside in the treatment of severe G-negative infections. Intensive care unit’s (ICU) patients present a large pharmacokinetic variability. The aim of our study was to provide a validated pharmacokinetic model of AMIK in ICU patients by using sparse data collected during routine clinical care. 
Materials and Methods: AMIK was administered intravenously over 0.5 h at once daily dosing regimens. A mixed-effect modelling (NONMEM) approach was used to fit the data. At first, the pharmacokinetics of AMIK was studied in 59 patients (201 serum concentrations). Demographics, clinical and biological covariates were tested for evaluating their influence : age, gender, weight, height, fever, general pathology, creatininemia, creatinine clearance, protidemia, uremia, leukocytes, hemoglobinemia, CRP, PLA2, simplified acute physiology scores (SAPS I et II). Concomitant medications were also studied : furosemide, vancomycin, corticosteroids, non-steroidal anti-inflammatory drugs and catecholamines. A second group of 23 patients (92 serum concentrations) was used for the validation. 
Results: An open two-compartment PK model with zero-order input was used to describe the kinetics of AMIK. The statistical model chosen to describe the inter-individual variability (IIV) in pharmacokinetic parameters and the residual error was a proportional one. This model was used to predict serum AMIK concentrations in the validation group which did not differ from the model population. To determine the predictive performance of our model we have compared the mean ± SD observed (18,2 ± 19,9 mg/L) and predicted values (18,8 ± 20,0 mg/L) by computing bias (0,618; IC: -1,338 ; 2,574), precision (9,54 mg/L), average fold error (1,63) and correlation (r=0,8850). The final population model was : TVCL = (1 + 0.029 x CLCR) x (1 – 0.0154 x IGS1); TVV1 = 0.294 x WT; TVQ = 5.52; IF(PLA2.GT.10) TVQ = 2.59; TVV2 = (1.23 x CLCR) x (1 – 0.0347 x IGS1) The mean population parameters and their IIV (CV %) obtained for the 82 patients are as follows : clearance (3 L/h, 28%), initial volume of distribution (22 L, 18 %), inter-compartmental clearance (4.3 L/h, 73 %) and peripheral volume of distribution (66 L, 59 %). 
Discussion-Conclusion: The mean values obtained for AMIK pharmacokinetic parameters are consistent with reported values in ICU patients. The covariates included in the model explain a part of the IIV in the pharmacokinetic parameters. Our model will permit to adjust AMIK dosage regimen in clinical routine. 

Assessment of the Predictive Performance of a New Population Pharmacokinetic Model For Trastuzumab (Herceptin) and Simulation of Trastuzumab Steady-State Exposure During Long-Term Weekly Dosing.

Jian-Feng Lu and René Bruno
Pharmacometry Group, Clinical and Experimental Pharmacology Division, Genentech Inc. South San Francisco CA.
poster
Purpose: To assess the predictive performance of a new population PK model for trastuzumab and to investigate inter-patient variability of trastuzumab exposure at steady-state (SS) after weekly dosing of Herceptin. 
Methods: The PK of trastuzumab following long-term weekly dosing in HER2 overexpressing metastatic breast cancer patients has been reevaluated using the population approach (1). The terminal half-life was 28.5 days (95% CI, 25.5-32.8 days), longer than previous estimates (5.8 days). In addition inter-patient variability and covariate effects on trastuzumab PK parameters were estimated. The performance of the model in predicting trastuzumab exposure (trough levels) was evaluated in 416 patients who participated to trastuzumab single-agent and combination studies by using a simulation-based model checking. Several statistics of observed levels were compared to their distribution from 100 replicates of data sets simulated under the model. To assess the magnitude of inter-patient variability of SS trough levels, trough levels were simulated at SS for 1000 patients using the model (patients characteristics bootstrapped from the actual database of 416 patients). All the simulations were performed using the NONMEM program. 
Results: The model adequately predicted 25th, 50th (median), 75th percentiles, mean and standard deviation of observed trough levels demonstrating the usefulness of the model in predicting trastuzumab exposure and its variability. The inter-patients variability (%CV) of SS troughs in 1000 simulated patients was 67.6%. The variability due to covariate effects (patient weight, number of metastatic sites, plasma level of extra-cellular domain of the HER2 receptor) was 28.7%. Expected trough concentrations exceeded 20 ng/mL (the efficacy threshold level) in most of the patients (92.5 %). 
Conclusion: The new trastuzumab population PK model provides an operational tool to simulate trastuzumab exposure during Herceptin treatment of MBC patients, explore PK-clinical response relationships and simulate alternative dosing regimen (Q3W) for trastuzumab. 
1 - Washington C.B., Lieberman G., Liu P., Fox J.A., Bruno R. A population pharmacokinetic model for trastuzumab following weekly dosing. Clin. Pharmacol. Ther., 71 (2), P12 (abstract MPI-30), 2002. 

Discussion of criteria for evaluating the quality of glucose clamp studies

Andreas V. Groth, Mikael S. Thomsen, Morten Colding-Jørgensen & Erik Mosekilde
Technical University of Denmark & Novo Nordisk A/S
poster
The pharmacodynamic (PD) action of insulin and insulin analogues is the lowering of the blood glucose concentration (BG) by increased glucose uptake into the body tissues. The “golden standard” test of the PD time profile of any insulin analogue is a glucose clamp, in which the insulin analogue is administered to the test subject by the same route as intended for clinical use and BG is subsequently clamped, i.e. maintained approximately constant. This occurs by means of a variable Glucose Infusion Rate (GIR), by which one attempts to compensate as exactly as possible for the glucose disappearance from the blood induced by the insulin (analogue). If the compensation succeeds well, the GIR time profile may be interpreted as the analogue PD time profile and this is standard procedure. 
However, practical glucose clamping is imperfect: Some variation in BG occurs, and criteria for when circumstances may have deviated so much from the ideal clamping conditions that the PD time profile cannot be considered identical to the experimental GIR time profile are not well defined. In this study we discuss what deviations from ideal may significantly affect the pharmacological endpoints, i.e. the conclusions about the drug action that are drawn from the clamp study. We use the GIR-AUC (total amount of infused glucose) as our “case end-point” since GIR-AUC is generally a key end-point in glucose clamp studies. Based on these considerations, we propose criteria for evaluating “glucose clamp quality”, i.e. measures that we should attempt to minimise when doing a glucose clamp. Finally, we compare the performance of an automatic glucose clamp control system (the BIOSTATOR system) with that of a manual glucose clamp control system, both of them evaluated by the proposed criteria.

Population pharmacokinetics of long-term methotrexate in children with lymphoblastic leukemia

M.J. García1, D. Santos Buelga1,D. Aumente2, P. Gomez2 ,JC.Lukas1

poster
A high dose Methotrexate (HD MTX) protocol was used for long-term treatment of 37 children, 20 males and 17 females with lymphoblastic leukemia. The treatment consisted of administration of a fast followed by a slow perfusion of MTX with a mean dose of 1850 mg in 2 to 5 treatment cycles (mean 3.5) per child, with 2- 8 plasma concentration measurements (mean 3.3) per cycle. An index group of 30 individuals was used for population model development and the remaining 7 subjects were used for validation of the final covariate model. The index and validation groups had [mean (range)] AGE = 7.7 (1.2-16) and 7.6 (2 – 17) years and weight (WT) = 33 (9.5-80) and 35 (12-59) kg respectively. A bicompartmental pharmacokinetic model was fitted with the non linear mixed effects package NONMEM and the first order conditional estimation (FOCE) method, to obtain the distribution of the parameters of MTX in children. Covariate models were developed on a random subset of 30 children (830 concentrations) within population fits with age, body surface, height, sex and weight. The models were for central clearance, CL = 3.67 + 0.042WT (L/h) and central volume of distribution, Vc = 6.23 + 0.14.WT (L). For the typical child (CV%) CL= 4.42 (27% ) L/h and Vc = 9.73 (28%) L which implied a drop tin the interindividual variability of 27% and 32% for CL and V respectively, compared to the basic model. The covariate model was validated by predicting the concentrations in the remaining 7 patients (validation group). Bias was –1.65 (I.C. ) and precision was 7.38. The model could be used in children with this pathology as Bayesian prior for the individualized prediction of dose titration within the therapeutic protocol.

Phenytoin covariate models for Michaelis-Menten pharmacokinetics in adult epileptic patients

D. Santos Buelga1, M.J. García1, MJ Otero2, A. Martin Suarez1, A. Dominguez-Gil2, JC.Lukas1

poster
Phenytoin plasma concentration minima at steady state (Cmin) were monitored in 230 adult outpatients with epilepsy. The drug is metabolized by cytochrome P450 through a saturable process. The population was randomly divided into an index (n = 200; 620 x Cmin) group for model development, and a validation group (n = 30). The Michaelis Menten (MM) kinetics (average of 3 occasions per individual) was modeled with the first order (FO) nonlinear mixed effects method of NONMEM employing the steady state model of the rate of administration versus concentration, to determine the MM parameters. The maximum biotransformation rate (Vmax) was [typical population value (CV%)] 17.9 mg/h (28%) and the concentration at half the saturation rate (Km) was 4.4 mg/L (73%). The demographic covariates weight, age, height, sex as well as comedication with carbamazepine, phenobarbital and valproic acid were tested for their explicatory capacity of the interindividual variabilities. The final model was Vmax = 13.9 + 3.97*WT/67 mg/h (25%) (428 mg/day for the typical patient) and Km = 4.29 mg/L (68%) with a reduction in the log-likelihood objective function of 13.03 (chi-square significant at p<0.001) and a 11% reduction in the determinant of the covariance matrix. This model was validated in the remaining 30 patients (60 x Cmin) with bias (confidence interval) 0.03 (-.07, 0.13) and precision 0.16 (-0.47, 0.79).

Population Pharmacokinetics and Effects of Efavirenz in HIV Patients

C. Csajka(1), C. Marzolini(1), K. Fattinger(2), L.A. Décosterd(1), J. Fellay(3), A. Telenti(3), J. Biollaz(1), T. Buclin(1)
(1)Divison of Clinical Pharmacology, University Hospital CHUV, Lausanne, Switzerland; (2)Division of Clinical Pharmacology, University of Zürich, Switzerland; (3)Division of Infections Diseases, University Hospital CHUV, Lausanne, Switzerland
poster
Objectives: The reverse transcriptase inhibitor efavirenz is currently used at a fixed dose of 600 mg qd. Dosage individualisation based on plasma concentration monitoring might however be indicated. This study aimed to assess efavirenz pharmacokinetic profile and interpatient versus intrapatient variability in HIV positive patients to explore the relationship between drug exposure, efficacy and CNS toxicity and to build up a Bayesian approach for dosage adaptation. 
Methods: The population pharmacokinetic analysis was performed using NONMEM based on plasma samples from a cohort of unselected patients receiving efavirenz. With the use of a one-compartment model with first order absorption, the influence of demographic and clinical characteristics on oral clearance and oral volume of distribution were examined. The average drug exposure over one dosing interval was estimated for each patient and correlated with markers of efficacy and toxicity. The population kinetic parameters and the variabilities were integrated into a Bayesian equation for dosage adaptation based on a single plasma sample. 
Results: 235 patients contributed to 719 efavirenz concentrations. Oral clearance was 9.4 L/h, oral volume of distribution was 252 L and the absorption rate constant was 0.3 h-1. Of the covariates evaluated, the African ethnicity and drugs inhibiting the cytochrome P4503A4 showed an influence on efavirenz pharmacokinetics. A large interpatient variability was found to affect efavirenz relative bioavailability (CV 54.6%), while the intrapatient variability was small (CV 26%). An inverse correlation between average drug exposure and viral load and a trend with CNS toxicity were detected. This enabled the derivation of a dosing adaptation strategy suitable to bring the average concentration into a therapeutic target of 1000-4000 mg/L, to optimise viral load suppression and minimise CNS toxicity. 
Conclusion: The high interpatient and low intrapatient variability, along with the relationship with markers of efficacy and toxicity, make efavirenz a drug suitable for therapeutic drug monitoring. Individualisation of efavirenz dosage regimen based on routine drug level monitoring appears suitable for its optimal management. 

THE EFFECT OF COLLINEARITY ON THE SELECTION OF COVARIATES IN POPULATION PHARMACOKINETIC ANALYSIS

Jakob Ribbing and E. Niclas Jonsson
Uppsala University, Sweden
poster
Identifying covariate relations is usually an important part of the development of population pharmacokinetics/pharmacodynamics (PK/PD) models. This is commonly a time consuming task, especially if there is a large number of possible covariate relationships to investigate. However, with many potential covariates it is often the case that some, or many of them, are correlated, i.e. more than one covariate carry the same type of information.
The aim of this simulation study was to investigate the impact of correlated covariates on the power to identify the true covariate as well as on the bias in the estimated covariate coefficient. The investigation was carried out over a range of data set sizes, correlations and covariate strengths.
Data sets with 20 to 1000 subjects were investigated. For each data set size, 10,000 covariate datasets with five covariates each were created by sampling from a multivariate standard normal distribution. The true covariate was set up to have a strong, medium, weak and no correlation to the other four covariates, respectively. The latter four were constrained to have no correlation to each other. 
Data sets, in which each individual had three observations, were simulated using a one compartment, i.v. bolus model. The covariate influenced clearance according to one of several magnitudes (including no influence). Models with each of the simulated covariates influencing clearance and the model without any covariate were fitted to the data and the power to select the true covariate was recorded. The estimated coefficient for all covariates was also retained for further analysis.
The results show that the power to select the true covariate decrease as a function of the correlation to the competing covariate, with only a minor influence of the data set size and covariate strength. The relative bias in the coefficients decreased with increasing data set size and covariate strength while it increased with increasing correlation to competing covariates.

Population Pharmacokinetics of Theophylline during Paediatric Extracorporeal Membrane Oxygenation (ECMO)

Hussain Mulla, Fazal Nabi, Sanjiv Nichani, Richard K Firmin, Graham Lawson, David R Upton

poster
Introduction: Aminophylline is used to increase diuresis in critically ill children with fluid overload. ECMO is a life support technique used in the management of children with severe cardiopulmonary failure unresponsive to conventional treatment modalities including mechanical ventilation. However, ECMO is known to affect the disposition of drugs as a result of an expanded circulating volume and drug losses associated with the extacorporeal circuit. The purpose of this study was thus to determine the population pharmacokinetics of theophylline during ECMO from routine monitoring data. 
Patients and Methods: Retrospective and prospective data from 75 term neonates and children receiving aminophylline during ECMO were eligible for investigation.A total of 160 plasma concentrations,sampled at time intervals ranging 10 to 432 hours, were included. Drug concentrations were measured using the Olympus System, enzyme immunoassay OSR6412 (Olympus Diagnostica GmbH). Population PK analysis and model building using demographic and clinical covariables was carried out using WinNonMix (Version 2.0.1). 
Results: A one-compartment model with first order elimination associated to an additive error model was found to be the most suitable. Covariates collected were: Age (post natal in neonates) (median 39 (range 2 – 6205) days), bodyweight (median 4.0 (range 2.1 – 85) Kg), urea and creatinine (mmol/l), renal replacement therapy (e.g. Haemofiltration), ECMO flow rate, Veno-venous or Venoarterial ECMO cannulation, co-medication, c- reactive protein, congenital diaphragmatic hernia, cardiac disease and pneumonia. Of the covariables tested, bodyweight significantly influenced clearance and volume of distribution whilst age was also an important determinant of clearance, as adjudged by the differences in the minus 2 * log likelihood (p<0.005) and the residual error value. The final model parameters were estimated as: clearance (L/hour) = 0.023 * bodyweight + 0.000057 * Age (days), volume of distribution (L/kg) = 0.57. The interindividual variability in clearance and volume of distribution was 38%, and 40% respectively. The residual variance (additive error) corresponded to an estimated standard deviation of 3.5mg/L. 
Conclusion: This is the first report of population PK of theophylline in paediatric ECMO patients. The estimated clearance is significantly lower than previously reported in this age group. These differences are probably as a result of the expanded circulating volume, but also altered renal and hepatic physiology in this extremely critically ill group. Large interindividual variability also reflects the heterogeneous nature of patients treated on ECMO. 

Pharmacokinetics of the three main alkaloids present in the South American psychoactive beverage Ayahuasca after oral administration to healthy volunteers

Valle M, Riba J, Yritia M, Barbanoj MJ.
Institut de Recerca del HSCSP. Hospital de la Santa Creu i Sant Pau. 08025 Barcelona, Spain
poster
Ayahuasca is a South American psychotropic plant tea used since pre- Columbian times in the Upper Amazon and Orinoco River Basins. This tea is obtained from Banisteriopsis caapi and Psychotria viridis and combines monoamine-oxidase- inhibiting beta-carboline alkaloids (harmine, harmaline, and tetrahydroharmine) with N,N-dimethyltryptamine (DMT), a hallucinogenic agent showing 5-HT2A/2C agonist activity. Important individual differences have been observed under laboratory conditions in the subjective effect profile reported by volunteers after oral administration of ayahuasca. The objective of the present work was to characterize the pharmacokinetics of DMT (main psychoactive compound), harmaline and tetrahydroharmine after oral dosing with ayahuasca. 
Methods: Two oral doses of encapsulated freeze-dried ayahuasca (0.6 and 0.85 mg of DMT/kg) were administered to 18 healthy volunteers according to a double blind, crossover design. Plasma concentrations of DMT, harmaline and tetrahydroharmine were determined at different times by means of validated GC (DMT) and HPLC techniques. Pharmacokinetic analyses were carried out with NONMEM (version V), using first-order or first-order conditional estimation methods. Absorption was modeled as zero- or first-order processes, and sometimes as a combination of both processes with different lag times. Different linear and non-linear models (saturable, time-dependent) were investigated in order to describe drug elimination. To describe the distribution of the alkaloids, different compartmental models were employed. 
Results: DMT: A one-compartment model with first-order absorption and elimination processes from the central compartment best described the time course of DMT plasma concentrations. The estimated volume of distribution from the central compartment (V/F) and its relative standard error (%) were 3210 L (20), with an associated interindividual variability (IIV (CV (%)) of 82 (37). The total estimated plasma clearance (Cl/F) was 1300 L/h (13), with a IIV of 34 (33). Absorption was described as a dose-dependent process: ka=4.57 h-1 (70) for the low dose, and ka=1.78 h-1 (23) for the high dose; the associated IIV was 63 (70). The estimated lag time was 0.6 h (14) with an IIV of 22 (39). Harmaline: A one-compartment model with zero-order absorption and first-order elimination processes from the central compartment best fitted the time course of harmaline plasma concentrations. The estimated V/F was 1290 L (17), with an IIV of 48 (34). Estimated Cl/F was 658 L/h (22), with a higher IIV, 78 (58). The duration of the absorption for the low dose was estimated to be 1.48 h (7.5), after a lag time of 0.257 h (44). For the high dose, the duration of this process was longer, 2.59 (7.1) without lag time. Tetrahydroharmine: A one-compartment model with first-order absorption and elimination processes from the central compartment best described the time course of tetrahydroharmine plasma concentrations. The estimated V/F was 375L (30), with an IIV of 95(40). Cl/F was dose-dependent: 462 L/h (23) for the low dose and 335 L/h (20) for the high dose, with a high IIV, 91 (69). The estimated absorption ka was 0.189 h-1 (18) after a lag time of 0.696 h (14). 

ESTIMATING BIAS IN PARAMETERS FOR SOME NONMEM MODELS FOR ORDERED CATEGORICAL DATA

Siv Jönsson and Mats O. Karlsson
Uppsala University, Sweden
poster
Introduction Side effect data are commonly reported as ordered categorical data e.g. none, mild, moderate and severe. Oftentimes only a relative minor fraction of the patients experience a side effect, which may affect the estimation properties of the methods used. The present study aimed at investigating the bias in parameter estimates for models for ordered categorical data using NONMEM (1).
Methods A population logistic regression model for ordered categorical data was used for simulation and estimation within NONMEM. The model predicts for each individual observation, Yit, the probability of having a score that is greater than or equal to a given score m = 0, 1, 2, 3 and has the general structure
Pr (Yit = m|ETA) = exp(INT + ETA )/[1 + exp(INT + ETA)] 
where INT is the sum of THj (j=1 to m). ETA denotes the individual random effect which is assumed to be a symmetrically distributed, zero-mean random variable with a variance of OM2. 
Bias in the population estimates was studied based on Monte Carlo simulated data sets (n=100), each data set comprising 1000 patients with 4 observations each. The model given above was fitted to each simulated data set, followed by simulations of new data based on the parameter estimates.
Results and conclusions When nominal parameter estimates were chosen so that relatively even distributions between responses were obtained, NONMEM performed well and simulations under the estimated model parameters mimicked the real data. However, in cases where only a minor fraction of the observations was non-zero, one or more of the population estimates were highly biased, resulting in that simulations under the estimated model parameters did not reflect the observed data, see one example below. The bias appears to be linked to a non-normal distribution of estimated ETAs and increases with increasing value of OM2.
Parameter 	TH1	TH2	TH3	OM2	
Nominal value	- 8.25	- 2.43	- 2.86	40	
Estimated value 
mean (range)	- 9.28
(-9.71, -8.60)	- 2.86
(-3.38, -2.46)	- 3.30
(-4.08, -2.55)	113
(83, 141)	

	Fraction of observations = 0	Fraction of observations = 1	Fraction of observations = 2	Fraction of observations = 3	
Simulations based on nominal values
mean (range)	0.89
(0.87, 0.91)	0.054
(0.041, 0.073)	0.033
(0.024, 0.046)	0.020
(0.011, 0.029)	
Simulations based on estimated values
mean (range)	0.83
(0.81, 0.85)	0.066
(0.052, 0.077)	0.047
(0.035, 0.060)	0.061
(0.043, 0.077)	
1. Beal SL, Sheiner LB. NONMEM users guides. NONMEM Project Group. San Francisco: University of California at San Francisco; 1998.

POPULATION PHARMACOKINETIC ANALYSIS OF ZARNESTRA USING DATA FROM PHASE I CLINICAL TRIALS

Juan Jose Perez Ruixo; Vladimir Piotrovsky; Kenneth H. Cowan; Louis Weiner; Cornelis J.A. Punt; Martine Piccart.

poster
Objective: To perform a population pharmacokinetic (PK) analysis of the phase I clinical trial data of a new anticancer drug, after single and multiple doses of different drug formulations in healthy volunteers as well as cancer patients. 
Patients and Methods: Data from 12 healthy volunteers and 129 patients included in 6 phase I clinical trials were pooled. Subjects were treated with ZarnestraTM (orally and intravenously). Three different oral formulations (solution, capsule and tablet) were administered as a single dose or as multiple doses (b.i.d) in a range dose between 25 and 1300 mg. Data for 1, 2 and 24 hours intravenous infusions for different dose levels were also available. Full PK profiles were scheduled at least in two occassions for every patient. Moreover, trough levels were obtained for multiple dose regimen. A total of 3129 plasma concentrations were obtained and analyzed by a validated assay method. 
An open three-compartment linear disposition model with sequential zero and first order absorption process and lag time was fitted to the data. Interindividual and interoccassion variabilities were implemented through exponential error model. Measured concentrations and model predictions were transformed into logarithms. The error model was additive and included 2 variances to account for the residual variability of full PK profiles and trough levels. The estimation of the population parameters was done with the first order approximation method implemented in NONMEM V software. 
Body size parameters (weight, lean body mass, ideal body weight, body mass index, and body surface area), renal (creatinine clearance and glomerular filtration rate) and liver function tests (AST, ALT, AP, LDH and total bilirubine), trial, drug formulation, target population and disease stage were tested as covariates by graphical exploration followed by (one-by-one) the forward stepwise inclusion procedure. Finally, the significance of covariate fixed effects was tested by backward elimination. The p-value for retaining a covariate in the model was 0.01 at 1 degree of freedom, c 2 distribution. 
Results: The pharmacokinetics of the drug was proved to be dose- proportional in the wide dose range. Population PK parameters after tablet administration are shown in the table 1. Healthy volunteers have a higher clearance and volume of distribution in the central and peripheral compartments, as well as a higher absorption rate and a lower duration of the zero-order process than patients in the target population. Rate and extent of absorption are significantly different between drug formulations. AST is associated with the decrease in plasma clearance, and volume of distribution in peripheral compartment increased with body weight. 
Table 1. Population pharmacokinetics parameters of Zarnestra after IV and tablet administration.
Parameter	Mean (CV, %*)	IIV (CV, %)	IOV (CV, %)	
CL (L/h) 	22.6 (5.13)	33.32 (20.72)	26.55 (29.58)	
Vc (L)	66.4 (7.95)	43.01 (36.22)	-	
Q2 (L/h)	3.49 (14.13)	67.23 (33.63)	122.88 (45.17)	
V2 (L)	105 (10.19)	87.52 (32.51)	-	
Q3 (L/h)	20.7 (30.14)	-	-	
V3 (L)	27.6 (15.07)	-	-	
Ka (1/h)	1.21 (15.12)	146.29 (58.88)	110.45 (24.34)	
D (h)	0.84 (3.26)	93.43 (49.37)	15.62 (50.41)	
F (%)	0.35 (5.19)	48.06 (18.70)	50.20 (34.60)	
Lag (h)	0.08 (0.09)	285.66 (75.37)	389.87 (35.99)	
* CV (%): Coefficient of variation
Conclusion: A population PK approach is useful tool to integrate the knowledge gathered in phase I studies. The model developed will help in dose adaptation and will further be used in PK/PD modelling of therapeutic outcomes and adverse events.

Population PK/PD modelling of a new MAO-B inhibitor in young and elderly healthy volunteers.

J.B. Fau * & C. Dubruc *, F. Mentré **.
* : Sanofi-Synthelabo Research, Clinical Metabolism & Pharmacokinetics, Chilly-Mazarin, France.
poster
The aim of this work was to investigate the population PK/PD relationship of SSR, a new MAO-B inhibitor, in healthy volunteers using NONMEM V. Data from 5 phase I studies were used with a total of 3964 PK and 3699 PD observations in 84 subjects (66 young from 18 to 40 years and 18 elderly from 65 to 85 years) after single or repeated administrations at six different doses.
The PK model, based on previous individual analyses, was a two-compartment model with zero order absorption including a lag time (ADVAN3, TRANS4). A multiplicative model for the random effects was used for all parameters (CL, V1, Q and V2) but inter-individual variability had to be fixed to zero for ALAG and D1. The error variance model was additive and multiplicative. Possible covariates (chemical batch, study number, gender, age, weight, creatinine clearance) were evaluated using graphical analysis, scientific plausibility, statistical significance and OF decrease. Only three covariates (chemical batch, weight and age group) were successfully included in the final PK model, using the FOCE interaction method.
After definition of the PK model, PD data (platelet MAO-B activity inhibition expressed as pmol/min/109) were studied. Again based on individual analyses, an inhibitory Emax sigmoid direct pharmacodynamic model was assumed (E = E0 – [ (E0-Emax) * Cpg / (EC50g + Cpg) ] ). Multiplicative random effects were used on all PD parameters (Emax, E0 and EC50) but had to be fixed to zero for g. The error variance model was purely multiplicative. Two methods of estimation were implemented : sequential (PK parameters, intra and inter-individual variabilities fixed to the values estimated in the PK analysis) and simultaneous population PK/PD fitting. The estimated parameters were similar and age group was identified as a significant PD covariate with both methods. The best PK/PD run was obtained after simultaneous PK and PD estimation with a slightly lower OF (12 points) when compared to sequential. However, the computation time was very large (approximately 12 hr vs 8 hr for the sequential method).
For this rich data analysis, sequential and simultaneous PK/PD modelling provided similar results in terms of typical parameter values, variabilities and identification of significant covariates. The results will be used to evaluate sampling protocols for population analysis of phase IIb/III studies in patients.

Efficiency of Using Population Pharmacokinetics to Demonstrate Bioequivalence with Sparse Sampling in Cancer Patients- A Trial Simulation with Etoposide

Eric Masson, 1, Eliane Fuseau, 2, Valérie Cosson, 2
(1):ANAPHARM, Canada (2):EMF-Consulting, France
poster
Purpose Etoposide (VP16) is an antineoplastic agent used in various malignancies. Like many anticancer drugs, toxicities preclude testing VP-16 in healthy subjects. Current FDA guidances on bioequivalence (BE) are based on two stage approach with calculation of pharmacokinetic (PK) parameters by non-compartmental analysis (NCA), followed by standard statistical analysis using average BE. Several factors preclude applying these guidances in cancer patients: anemia limiting extensive sampling, sampling time which vary, and presence co- factors affecting VP16 PK. One alternative is to use population PK which allows estimation of BE parameters (AUC, Cmax) with confidence intervals. The objective of the simulation is to evaluate the effect of two sampling schemes (sparse versus extensive), and designs (complete vs incomplete) to assess BE of VP16 using NONMEM. 
Methods Monte-Carlo simulations and population PK analyses were performed using NONMEM. Using priors from the literature on VP16, plasma concentrations of VP16 were simulated in subjects receiving two formulations of VP-16 in a randomised crossover fashion. Six different scenarios were tested using 2 way crossover studies in 50 subjects. Each scenarios were simulated 100 times each without blocking, period or sequence effects: 3 scenarios with full PK profiles (12 points), and 3 scenarios with reduced PK profiles (7 points selected on D- optimality) with none, 25% and 50% of drop-out after one cycle of drop- out. BE was evaluated for Cmax and F based on the average BE criteria. Success rate defined as percentage of studies for which 90% CI for Cmax and AUC ratio are within 80-125%. 
Results Full and sparse sampling with no dropout yielded 100% success compared to 98% success rate for sparse sampling and 50% dropout. Conclusion Population PK analysis allows accurate assessment of BE despite reduced sampling, and partial study completion. Thus, this method offers a significant advantage over average BE in cancer patients. 

Modelling of the effect of carbamazepine on the pharmacokinetics of risperidone in psychotic patients of different phenotypes

Vermeulen, An and Piotrovsky, Vladimir
Johnson & Johnson Pharmaceutical Research & Development, a division of Janssen Pharmaceutica N.V.
poster
Introduction: Risperidone (RIS) is a well- known and widely used atypical antipsychotic drug, on the market for almost a decade now.
RIS is mainly metabolised by CYP2D6 to the active metabolite 9-hydroxy-risperidone. The sum of RIS and 9- hydroxy-risperidone constitutes the active antipsychotic entity or the ‘active moiety’ (AM). Since the activity of CYP2D6 is subject to genetic polymorphism, the population is divided in poor, intermediate and extensive metabolisers. 
Besides being used to treat schizophrenia, RIS’ value for the treatment of other diseases like bipolar mania either as add-on therapy to the currently used mood stabilizers or as monotherapy has been investigated. Carbamazepine, one of these mood stabilizers, is well-known to induce the activity of several cytochromes, and has a profound effect on the pharmacokinetics of RIS and AM.
Objectives: The objectives of the current population pharmacokinetic analysis were: 
•	to model the pharmacokinetics of RIS in subjects of different phenotypes; 
•	to compare two methods of phenotyping: one based on the metabolic ratio (AM to RIS clearance) and another one using the mixture model for RIS embedded in the population PK model; 
•	to model the effect of carbamazepine on the pharmacokinetics of RIS in each of these phenotypes. 
Methods and results: A two-compartment disposition model with zero-order followed by first-order absorption, and lag-time was implemented for both RIS and AM. It was fitted to the data of several clinical trials using NONMEM software, and individual empirical Bayes estimates of basic PK parameters were obtained. Individual metabolic ratios were calculated as CLAM/CLRIS where CLAM and CLRIS are AM and RIS clearance, respectively. The distribution of metabolic ratios was examined and each subject was assigned to one of the phenotypes. The individually assigned phenotype was included in the data set as a covariate, and the covariate model was built using the conventional method. Carbamazepine co-administration was demonstrated to have a significant impact on the apparent bioavailability fraction.
An alternative approach consisted of fitting a common model for RIS and 9-hydroxy-risperidone to plasma concentration-time data of both compounds. The model incorporated a mixture for the apparent RIS fraction converted into the metabolite. In this model, carbamazepine was shown to affect this fraction.

NONPARAMETRIC POPULATION ANALYSIS OF AMIKACIN PHARMACOKINETIC DATA IN A PEDIATRIC POPULATION.

Merle Y.(1), Treluyer JM* (2), Tonnelier S (2), Rey E (2), Pons G (2).
(1) INSERM U436, CHU Pitie-Salpetriere, Paris, France. (2) Pharmacologie Perinatale et Pediatrique, Universite Rene-Descartes, Hopital Saint Vincent de Paul, Paris, France.
poster
The aims of our work were: i) to describe amikacin pharmacokinetics in populations of neonates, infants and children; ii) to determine the extent to which various covariates accounted for interindividual variability; iii) to compare the performances in terms of nephrotoxicity and therapeutic efficiency of a once daily and a twice daily regimen in our population. Therapeutic drug monitoring data were retrospectively collected from 155 patients and analysed by the nonparametric maximum likelihood method (NPML), nine covariates being included in the analysis. We investigated the extent to which each covariate accounted for the variability of each parameter by calculating the relative expected reduction of variance of the parameter distribution associated with each covariate. The relationships (if any) between parameters and covariates were explored by a graphical method. Amikacin plasma concentrations were simulated from Bayesian individual kinetic parameter estimates for the two studied dosing schedules. Our results illustrate the high interindividual variability of both clearance and distribution volume. The role of postnatal age and body weight in explaining this variability was also emphasized as well as the influence of plasma creatinine on clerarance. For both schedules the percentages of subjects with predicted minimum concentrations below 10 mg/L were close to 100%. In contrast the percentage of patients with a ratio "predicted maximum plasma concentrations/MIC" greater than 8 was higher for the once daily regimen than for the b.i.d. regimen for the considered MIC values. Since this threshold ratio is related to the treatment efficiency this result emphasizes the benefit of the once daily regimen. 

THE USE OF A STOCHASTIC MODEL FOR DATA EXHIBITING HETEROGENEOUS PHARMACOKINETICS

L.CLARET(1), P.MACHERAS(2), N.SIMON(3), A.ILIADIS(4)
(1)Pharsight Corporation, Argentum, 2 Queen Caroline Street, Hammersmith, London W6 9DT
poster
A stochastic compartmental model was developed to describe heterogeneous elimination kinetics of drugs. It is a probabilistic transfer model with a gamma distributed probability intensity coefficient for drug elimination. This model was compared to the traditional compartmental deterministic model in a population analysis of cyclosporin data from 52 patients receiving cyclosporin as a 2-hr intravenous infusion. Several methods (FOCE, two-stage) were used to estimate model parameters. The results showed that the stochastic model, although simpler than the compartmental deterministic models, is more flexible and consistent, and gives a better fit to the kinetic data of cyclosporin than the compartmental deterministic models.

Population pharmacokinetics of vinflunine from phase I data and evaluation of population sampling designs for further clinical development

L. Nguyen (1), S. Retout (2), F. Mentré (2), P. Variol (1) and C. Puozzo (1)
(1) Clinical Pharmacokinetic department, Institut de Recherche Pierre Fabre, Castres, France (2) Dpt of Biostatistics and Epidemiology, INSERM U436, University Hospital Bichat, Paris, France
poster
Vinflunine (Javlor(r)) is a novel semi-synthetic vinca alkaloid under development. Vinflunine is administered by short IV infusion and in vitro has demonstrated a superior anti-tumor activity to other vincas from a panel of 11 human xenografts. Extensive blood sampling per patient was performed in three phase I studies (n=59 patients), allowing to develop a first population PK model. Data were analysed using the NONMEM program. The vinflunine concentration-time data were best described using a linear pharmacokinetic model with four mamillary compartments (ADVAN 6 subroutine). Eight pharmacokinetic parameters were estimated with a good precision for the fixed effects (SE < 15%) and an acceptable precision for the random effect parameters (SE < 47%). Vinflunine after IV infusion was characterized by a high clearance (39.2 l/h) and large volumes of distribution (V1=16.5 l, V2=105 l, V3=421 l and V4 = 669 l). Interindividual and inter-occasion (IOV) variabilities on the clearance were 25% and 11%, respectively. After completion of phase I trials, population sampling designs with limited number of samples per individual must be planned for further clinical development. Selection of informative data should be made carefully to ensure a successful population study, taking into account the constraints of phase II/III clinical studies for which outpatients are recruited. Indeed, only restricted admissible sampling times are allowed and they often vary in few specific sampling windows circumscribed by hospital visiting hours. Population designs for vinflunine were assessed using an extension of the PFIM S-plus function [1,2]. Based on the recent development of the Fisher information matrix for non linear mixed-effect model, PFIM offers a direct and easy evaluation of a large set of possible sampling designs for a given population analytical model. However, the four-compartment model of vinfluine was only described by differential equations which then required to extend PFIM to this case. Therefore, based on samples of 50 to 100 patients, several balanced designs with four samples per individual were evaluated. Thanks to this approach, some practicable sampling designs were defined to obtain acceptable precision for the parameters of interest. Despite that PFIM does not take into account of the covariates influence and IOV, it provides a guideline on the number of patients, the number of sampling times and their allocation to perform population analyses, avoiding thus cumbersome simulations. 
[1] Retout S, Duffull S, Mentré F. Development and implementation of the population Fisher information matrix for evaluation of population pharmacokinetics designs. Comput Meth Prog Biomed, 2001, 65:141-51 
[2] http://hermes.biomath.jussieu.fr/pfim.htm 

Population PK Modeling of drugs exhibiting less than proportional increases in pharmacokinetics relative to increasing doses

Xuejun Chen, Suresh Mallikaarjun, Zhao Wang, Steven L. Bramer
Otsuka Maryland Research Institute, 2440 Research Blvd., Rockville, MD 20850
poster
Purpose: To explore the approach to modeling drugs exhibiting less than proportional increases in pharmacokinetics relative to increasing doses.
Methods: Data from 11 studies in healthy volunteers, with doses ranging from 5mg to 240mg of compound X, were used for a population PK analysis using NONMEM. The PK of compound X appeared to be nonlinear with Cmax and AUC increasing less than proportionally with increasing of dose. In order to model the less than proportional increase in plasma concentrations, several approaches were attempted: 1) expressing ka as function of dose; 2) expressing ka as step function of dose; 3) determining the inflection point for nonlinearity. These were evaluated by examining the objective function and diagnostic plots. 
Results: Objective functions are 34800 for expressing ka as function of dose, 33725 for expressing ka as step function of dose and 33620 for determining the inflection point of nonlinearity respectively. Splitting pharmacokinetic parameters by dose best described the nonlinear PK of compound X. 
Conclusions: For drugs exhibiting less than proportional increases in pharmacokinetics, the best model describing compound X is to split pharmacokinetic parameters based upon the inflection point.

Population pharmacokinetics of cyclophosphamide and its metabolites in hematopoietic stem- cell transplantation patients

A.A. Yao(a), J.T. Slattery(b,c), G.B. McDonald(c), and P. Vicini(a)
(a)Resource Facility for Population Kinetics, University of Washington, Seattle WA; (b)The Department of Pharmaceutics, University of Washington, Seattle WA; (c)Fred Hutchinson Cancer Research Center, Seattle WA
poster
Background: Cyclophosphamide (CY) is an alkylating agent frequently used in the treatment of malignancy and in preparative regimens for hematopoietic stem-cell transplantation. CY is a prodrug that is oxidized to 4- hydroxycyclophosphamide (HCY) at therapeutic concentrations. This is a reaction primarily catalyzed by CYP2C9 and CYP3A4 in human liver(1). HCY is the major active circulating metabolite that enters cells and decomposes to phosphoramide mustard and acrolein. Alternatively, HCY is detoxified to carboxyethylphosphoramide mustard (CEPM) by aldehyde dehydrogenase 1 (ALDH1A1). The formation of CEPM from HCY is the most important metabolic detoxifying pathway of HCY(2,3). CY is also oxidized to deschloroetyl cyclophosphamide, although this reaction accounts for little of CY disposition in humans. 
Objectives: [1] To develop an integrated mechanism-based population pharmacokinetic model for CY and its activated metabolites, namely HCY, and CEPM in hematopoietic stem- cell transplant patients. [2] To identify the mechanisms of the effects of the enzymatic autoinduction on CY metabolism and the decrease in human ALDH1A1 activity after CY administration. Methods: Patients 147 patients scheduled to receive unrelated donor bone marrow transplants were studied under a protocol approved by the Institutional Review Board of the Fred Hutchinson Cancer Research Center (Seattle, WA). Patients received 1-hour intravenous infusions of 60 mg/kg cyclophosphamide daily for 2 days, followed by 12-14.4 Gy total body irradiation. Blood samples were obtained just before CY infusion was given, at 0.5, and 1 hour after the beginning of the infusion, and at 1, 3, 6, 8, and 24 hours after the end of the infusion on both day 1 and 2 of treatment. Plasma concentrations of CY, HCY, and CEPM were determined as described previously(1). Data analysis The population pharmacokinetic analysis was conducted with the NONMEM(4) software, version V (Globomax, MD) and the first-order method. Interindividual variability of parameters was modeled using an exponential error model. An integrated model for the pharmacokinetics of CY, HCY, and CEPM was developed which included autoinduction(5) of CY oxidation to HCY and inhibition of ALDH1A1 activity after CY administration. 
Results and Discussion: Preliminary results indicated that the elimination of CY was best described by a non-inducible route and an inducible route leading to HCY formation. The inducible clearance was mediated by a hypothetical increase in enzyme concentration. The volume of distribution, non- inducible and initial inducible clearances of CY were: (estimate ± S.E.) 0.70 ± 0.01 l/kg, 0.0051 ± 0.0007 l/hr/kg, and 0.030 ± 0.001 l/hr/kg, respectively. The enzyme followed a zero-order formation, with an Emax- type decrease of the first-order rate constant describing elimination of CY with CY concentration: the induction half-life of the enzyme and the first-order rate constant of HCY elimination were estimated to be 9.18 hr, and 178 ± 16 hr-1, respectively. The inhibition of CEPM formation by HCY was described by the amount of ALDH1A1 enzyme. The hypothetical enzyme concentration followed a zero-order formation, and its elimination was proportional to the product of ALDH1A1 and HCY concentrations: the formation and elimination constants of CEPM were estimated as 2.18 ± 0.09 hr-1, and 0.94 ± 0.03 hr-1, respectively. The random effects for the non-inducible, inducible clearances of CY, elimination rate of HCY and zero-order formation rate constant of enzyme were (CV%): 84%, 38%, 28%, and 57%, respectively. Residual unknown variabilities were estimated using additive models for CY and CEPM, and a combination of proportional and additive errors for HCY. The estimated residual variabilities were: 59.7 mM (CY), 44.4% and 2.33 mM (HCY) and 1.85 mM (CEPM). This integrated model enabled the assessment of the complex pharmacokinetics of CY and may help to optimize the dose ranges in order to achieve engraftment without causing undesired effects. 
References: 
(1) S. Ren, T.F. Kalhorn, G. B. McDonald, C. Anasetti, F. R. Appelbaum, and J.T. Slattery. (1998) Pharmacokinetics of cyclophosphamide and its metabolites in bone marrow transplantation patients. Clin. Pharmacol. Ther. 64: 289-301. 
(2) S. Ren, T. F. Kalhorn and J. T. Slattery. (1999) Inhibition of human aldehyde dehydrogenase 1 by the 4-hydroxycyclophosphamide degradation product acrolein. Drug Met. Dispos. 27(1): 133-7. 
(3) S. Ren, and J. T. Slattery. (1999) Inhibition of carboxyethylphosphoramide mustard formation from 4-hydroxycyclophosphamide by carmustine. AAPS PharmSci. 1(3): article 14. 
(4) S. Beal, and L. Sheiner. NONMEM Users Guide. University of California, San Francisco, 1992. 
(5) T. Kerbusch, A.D.R. Huitema, J. Ouwerkerk, H. J. Keizer, R. A. A. Mathôt, J. H. M. Schellens, and J. H. Beijnen. (2000) Evaluation of the autoinduction of ifosfamide metabolism by a population pharmacokinetic approaching using NONMEM. Br. J. Clin. Pharmacol. 49: 555-61.

Information indexes for exploratory data analysis in population pharmacokinetics

P.BAILLE-ALBERT (1), O.PETRICOUL (1), E.FUSEAU (1), A.ILIADIS (2)
(1) EMF Consulting France, CEEI Provence, Aix-en-Provence (2) EA-3286, Faculty of Pharmacy, University of Méditerranée, Marseille
poster
Indexes derived from information theory were used to select the most appropriate model for the statistical distribution, to detect atypical individuals, and to screen influential covariates. These indexes could be complementary tools to the existing statistical and graphical techniques for population pharmacokinetic data analysis. Applied to explore observational data, the information indexes were used on the individual empirical Bayes estimates obtained in one-stage data analysis by the nonlinear mixed effect model. The rationale for using these indexes is shown using validation data for a drug under development.

Pooled PK analysis of Interferon-beta-1a (Rebif), data obtained in healthy subjects and in patients.

Sophie Glatt1, Olivier Petricoul1, Ciara Rossier2, Quyen T.X Nguyen2, Alain Munafo2, Timothy Goggin2, Mauro Buraglio2, and Eliane Fuseau1
1 EMF-Consulting, France; 2 SERONO SA International, Geneva switzerland
poster
Introduction and Objectives: Recombinant human interferon-beta-1a (Rebif) is currently used for the treatment of multiple sclerosis and is being investigated in other autoimmune diseases. The objective of the present PK analysis is to integrate all the available knowledge about the pharmacokinetics of interferon-beta-1a (IFN) in healthy subjects and in patients, including the relationships between pharmacokinetics and covariates such as route of administration, formulation, dosage, hematological parameters, demographics, etc… 
Methods: Rich and sparse data were available from healthy subjects and patients who received Rebif. A total of 435 subjects from 11 studies were included in the analysis. Rebif was administered at the doses of 22 µg, 44 µg, 66 µg and 88 µg by various routes (IV, SC and IM). The concentration of IFN was determined using a Toray enzyme linked immunosorbant assay (Elisa). The limits of quantification and detection were set to 2.5 IU/mL and 1 UI/mL, respectively. Concentration-time pooled data were analyzed by a population approach using NONMEM. 
Results: The SC, IM and IV data were fitted simultaneously to a 2-compartment model. Combinations of first order and mixed absorption were investigated to describe the absorption process. The residual error model was proportional and relevant covariates were explored once the base model has been established. The results of this analysis will be presented in the poster. 

Symmetry and coverage of confidence intervals for a population PK model.

Lars Lindbom, Mats O. Karlsson, E. Niclas Jonsson
Uppsala University, Sweden
poster
Standard error estimates give an indication of the quality of model parameter estimates and are useful tools in hypothesis testing. It is therefore important to evaluate the coverage and symmetry properties of confidence intervals derived from standard error estimates given by standard population modeling regression tools. The aim of this study was to assess these properties of some standard errors given by NONMEM.
The FO method of NONMEM was used for simulation and estimation of a one-compartment pharmacokinetic model with proportional and additive residual error model and IV-bolus administration. Data set size varies in number of subjects (25, 50, 100, 250, 600 and 1000) and number of samples per subject (2, 3 and 4). 2000 point and interval estimates of structural and variance parameters was recorded for all permutations of these data set sizes as well as 20, 30, 40 and 50 % magnitude of proportional error (CV). Bias in point estimates as well as coverage and symmetry in interval estimates at the 80, 90 and 95% confidence level was computed.
Under the assumptions regarding algorithm and model structure, better coverage, symmetry and bias are obtained with increasing number of subjects given the number of samples for each subject. The size of the proportional error does not seem to affect the quality of the bias, coverage and symmetry.

Retrospective Population Pharmacokinetics Of Cetirizine In Infants And Children

Ziad Hussein (1), Maria Pitsiu (1), Oneeb Majid (1), L. Aarons (2), A. Stockis (3) and M. de Longueville (3)
(1) Medeval Ltd and (2) University of Manchester, Manchester, UK, and (3) UCB Pharma, Braine-l’Alleud, Belgium
poster
This population analysis characterises the pharmacokinetics of cetirizine in infants and children using data pooled from six clinical trials following either single or multiple dose administration for up to 52 weeks. Cetirizine plasma concentration data was used for non-linear mixed effects modelling using the NONMEM program. Data from 112 children, aged 6 months to 12 years, were obtained. A one-compartment open model with first-order absorption and elimination was fitted to the plasma profiles. 
The effect of age, weight, body surface area, gender and CLcr on CL/F and V/F was examined. 
There were statistically significant associations between CL/F and both age and gender and between V/F and age, given by the following equations: 
Male children: CL/F (L/h) = 0.771 + 0.12 AGE
Female children: CL/F (L/h) = 0.592 + 0.12 AGE
Male and Female Children: V/F (L) = 4.00 + 1.42 AGE 
No other statistically significantly associations were found. The population estimate of CL/F for an average age of 7 years is 1.61 L/h and 1.43 L/h for male and female children, respectively. The population estimate of V/F is 13.9 L. The %CV of the variance parameters ranged from 21.8% to 37.2%. In conclusion, the current strategy of stratifying the dosage regimen of cetirizine in children by age is justified by the present analysis.

Population pharmacokinetics model validation using Kinetica

Xiaofeng Wang and Siu-Kei Tin
InnaPhase Corporation, Philadelphia, PA, USA
poster
Purpose: To investigate the algorithms of population modeling and validation implemented in Kinetica applied to both rich data and sparse data.
Method description: Datasets for both modeling and validation were generated using Matlab. The simulated data sets are split into two groups either manually or by randomization: one group, called the test group, is used to build the model; and the other, called the validation group, is used to validate the model. 500 datasets were simulated with 20% of inter-individual variability (normal distribution) and 20% of proportional residual error. The sampling times for rich data are 0.1, 0.5, 1, 3, and 5 for each subject. Sparse datasets were made with two sampling time between 0.1 to 8 hours. Both modeling and validation were performed on rich datasets and sparse datasets. In one case, 400 datasets were used to build the model, and the remaining 100 were used as validation datasets; in another case, 40 datasets were used to build the model, and the remaining 460 were used as validation datasets.
Two methods are implemented in Kinetica for model validation: Concentration method and parameter method. In the concentration method, parameter values for subjects belonging to the validation group were obtained using results from the test group (both parameter values and covariable equations) combined with the covariables information of the subjects in the validation group. Then, the concentration profiles of the individuals in the validation group, called Ci,j,pred, together with 95% confidence interval, were predicted. The validation was made through concentration deviation of predicted from observed values. They were presented as both individual concentration deviations and the mean square errors.
In the parameter method, results (both parameter values and covariable equations) obtained from the test group using EM algorithm were applied to Bayesian fit (E-step) on the validation datasets. The individual parameters obtained from this step (E-step) are called Pj,obs. If there are no covariable equations, the deviation of Pj,obs from population parameter (Ppred) obtained from EM on test group will serve as the criterion for model validation. If there are covariable equations, the predicted individual parameter value, called Pj,pred will be obtained from the covariable equations (obtained from the test group) combined with the covariable information of each subject in the validation group. Then, the deviation of Pj,obs from Pj,pred will serve as the criterion for model validation. 
In either method, the results are displayed both in spreadsheet form and in graphical form for easy comparison and visualization.
Results: For both rich datasets and sparse datasets, the parameter values obtained from model building agreed with the true parameter values used to simulate the datasets. The frequency histograms for both parameters and residuals indicated clearly the expected normal distribution. Model validation using either parameter method or concentration method also demonstrated that the results from model building are correct within inter-individual and intra-individual variability, either for sparse data or rich data. 
Conclusions: The population algorithm implemented in Kinetica appears to perform correctly with the simulated datasets, within statistical errors. However, to further validate the performance of the algorithm in Kinetica, more scenarios need to be investigated.

THE USE OF PHYSIOLOGICALLY BASED PHARMACOKINETIC (PBPK) MODEL IN DRUG DEVELOPMENT

PERDAEMS LAMBERT N.(1), BOUZOM F.(1), FREIDIG A.(2), SOLBES MARCHETTI M.N.(1), JOCHEMSEN R.(3), and WALTHER B.(1)
(1) Technologie SERVIER (Orléans-France)
poster
In PBPK models, the kinetics of a drug is related to physiological parameters (such as blood flow and tissue size) and to drug specific parameters (such as enzyme kinetics and tissue partitioning coefficients). With this type of models, pharmacokinetic profiles in man can be predicted using data of in vitro experiments with human material (microsomes e.g.) and/or in vivo experiments in other species, which is especially useful in an early stage of development.
Later in the development, PBPK can help to predict drug-drug interactions from other in vitro parameters (Vmax, Km, inhibition constant…).
The present study was performed to evaluate the PBPK approach to predict drug-drug interactions for a compound in phase III, ivabradine. That compound is mainly metabolised by the cytochrome P450 3A4 which is involved in drug metabolism of many drugs. So, the potential for drug-drug interactions to occur is substantial and the result can be of great clinical significance.
First, a PBPK model was built to describe pharmacokinetics of ivabradine when administered alone. Five tissue compartments (liver, adipose, heart, richly and poorly perfused tissue) and blood were included in this PBPK model. Good predictions for blood concentrations after intravenous and oral administrations were obtained with this model. 
In the same way, taking benefit from a collaboration project with TNO, PBPK models were built to predict blood and tissue profiles of potential inhibitors (verapamil and ketoconazole) when they are not co-administered.
Then, combination of the two PBPK models was realised to predict both, ivabradine and potential inhibitor concentrations when they are co-administered.
The influence of different parameters such as the unbound tissue fraction, the partition coefficient, the inhibition constant was evaluated by using sensitive analysis. The results of the simulations were compared to observed concentrations from in vivo studies in healthy volunteers.

PHARMACOKINETIC MIXED EFFECTS MODELLING OF S 16257 AFTER ORAL ADMINISTRATION IN THE BEAGLE DOG; COMBINED ANALYSIS

L. Del Frari, F. Bouzom, B. Walther and R.Jochemsen
Technologie Servier (Orléans, France)
poster
The objectives of the study were to build a population pharmacokinetic model for S 16257 after oral administration in dogs in order to "summarise" the pharmacokinetics of S 16257 in dogs, to identify factors causing interindividual variability in pharmacokinetics and to quantify the influence of these factors on pharmacokinetic parameters. Data used were taken from all pharmacokinetic and toxicokinetic studies including single and repeated oral administration with different treatment duration in the beagle dog. The database consisted of 2158 concentrations in 128 dogs (64 females and 64 males). The doses (expressed as base form) ranged from 0.225 to 41.8 mg/kg (from 1.60 to 376 mg) and were administered once or twice a day. The body weight ranged from 5.70 to 13.1 kg. 
The S 16257 concentration-time data in the beagle dog were fitted by a two-compartment model with a first order absorption using the NONMEM computer program. This model was defined in terms of apparent clearance (CL/F), apparent volume of the central compartment (Vc/F), apparent intercompartment clearance (Q/F), apparent volume of the peripheral compartment (Vp/F) and absorption rate constant (ka). Inter-individual variabilities were estimated for all the parameters except for Vp/F. A same inter-occasion variability was attributed to the distribution and elimination parameters in order to estimate an inter-occasion variability on the bioavailability. An inter-occasion variability on ka was also estimated.
No time effect was observed for the pharmacokinetics of S 16257 in the dog and single and repeated administration could be fitted together.
Different ka and a relative bioavailability existed between the two administrations in the day. The dose, the duration of the treatment, the body weight and the sex did not influence CL/F and Vc/F and none of the covariates tested was found to influence significantly any other parameter. The influence of the time of the administration in the day could be summarized as follows: the absorption rate after the first administration was about 5-fold higher than after the second administration while the exposure after the first administration was only about 10 % higher than after the second administration. This difference was attributed to a food-interaction as the food was given between the 2 administrations (about 4 h after the first administration and about 4 h before the second administration in the day).
This population model allowed to clearly define the time and dose effect, as well as the important covariates on S 16257 pharmacokinetics in the dog in the dose range studied during the development of S 16257 and could be used to estimate individual S 16257 pharmacokinetic parameters by bayesian feedback for studies using sparse sampling times in dogs.

GAUSS HERMITE QUADRATURE IN POPULATION PARAMETERS ESTIMATION. APPLICATION TO THE DETECTION OF SUBPOPULATIONS

A. DIOT(1,2), C. LAVEILLE(2), N. FREY(2), R. JOCHEMSEN(2) & A. MALLET(1)
(1) INSERM U436, Dept Biomathematics, CHU Pitié Salpetrière, 91 bd de l’Hôpital, 75013 Paris, France; (2) Institut de Recherches Internationales Servier, 6 place des Pléiades, 92415 Courbevoie Cedex, France
poster
Several methods have been proposed for estimating the different parameters entering the non-linear mixed effects models in population pharmacokinetics/pharmacodynamics. This work presents a methodological approach which allows to obtain a better approximation of the likelihood function. Its principal aim is to compute this likelihood up to a satisfactory and adjustable degree of approximation. Our hypothesis is that the accuracy of this approximation is likely to point out subtle features such as multimodality. Indeed, one feature of the method is the detection of heterogeneities or subpopulations with the introduction of mixture in the distribution of the random parameters. 
In order to obtain good estimations and detection of heterogeneities, we propose an approach using the Gauss Hermite numerical quadratures. Thanks to this quadrature, we can express the integral-based individual likelihood according to an easy way to compute expression: weighted values of the individual likelihood function calculated for tabulated nodes (Stroud and Secrest,1966). Starting from the basic quadrature formula, we show that several adaptations are necessary to render this approach efficient in population pharmacokinetic/pharmacodynamic settings : it is necessary to shift and scale the space of the random parameters to obtain accurate estimates of the likelihood. Proposed methods are based on arguments given by Liu and Pierce (1994) and Pinheiro and Bates (1995).
In this work, we point out how this method is able to detect subpopulations in clinical studies. It relies upon the example of a pharmacokinetic model of an anti-diabetic drug for which we study the problem of different classes of clearance. To understand this classification we try to explain it using the covariates of the patients. A second example presents a pharmacodynamic model of this drug, the salient question being the detection of responder and non responder patients.

Population pharmacokinetic and pharmacodynamic modeling of etanercept using logistic regression analysis

Howard Lee, Hui C. Kimko, Mark Rogge, Diane Wang, Ivan Nestorov and Carl C. Peck
Georgetown University, Immunex Corporation
poster
Objectives: To develop a population pharmacokinetic (PK) and pharmacodynamic model of etanercept in patients with rheumatoid arthritis (RA), using the American College of Rheumatology response criterion of 20 % improvement (ACR20) as a binary clinical outcome variable. 
Methods: Concentration data from 25 subjects administered 25 mg subcutaneous (SC) etanercept twice weekly for 24 weeks (42 samples per subject) were pooled with concentrations from 77 subjects (3 samples per subject), enrolled in a 24- week, randomized, double-blind study comparing 25 mg and 50 mg SC etanercept twice weekly. The cumulative area under the concentration-time curve (AUC) was calculated and used as an exposure variable. ACR20 was the binomial clinical outcome. ACR20 data from another 80 placebo- treated patients enrolled in a randomized and double-blind phase III study were used to describe the placebo time course of ACR20. A logistic regression analysis using NONMEM was applied to describe an exposure-time-effect relationship, and the 95% confidence interval (CI) was constructed by bootstrapping 1,000 times. 
Results: The population standard of apparent clearance was 0.117 L/hr (95% CI: 0.108-0.130 L/hr) for Caucasian females and 0.138 L/hr for Caucasian males (95% CI: 0.118-0.163 L/hr). The interindividual and interoccasion variability were 41.1% and 27.6%, respectively. The absorption half-life was 20.9 hrs and elimination half-life was 95.4 hrs. The model- predicted percentage of patients achieving ACR20 at 6 months following 25 mg SC twice weekly dosing was 54.9%, comparable to the observed 52.9%. 
Conclusion: The population PK analysis confirmed that etanercept is slowly absorbed and then eliminated after SC administration and the logistic model linking cumulative AUC with ACR20 adequately characterized the time course of clinical improvement in RA patients receiving etanercept. 

Mixture models : simulation and estimation with NONMEM

F.Hourcade- Potelleret *, C. Laveille *, M.Tod ** and R. Jochemsen *
* Institut de Recherche International Servier, 6 place des Pléiades 92415 Courbevoie cedex ; ** Hôpital Avicennes, 125 rue stalingrad 93009 Bobigny
poster
The pharmacokinetic parameters are usually assumed to be normally or log-normally distributed in the population. If a pharmacokinetic parameter is bimodally distributed, one can use the $MIX routine in NONMEM : the $MIX record describes the probabilities of each subpopulation for a mixture population. For instance, the population is divided into two subpopulations for the catalytic activity of the cytochrome D6 : they are "fast hydroxylators" and "slow hydroxylators" (nsubpopulations = 2). In this case, the $MIX routine is able to evaluate the proportion of each subpopulation.
The purpose of the task was to test the accuracy of the $MIX routine for describing the mixture probabilities of a mixture model. Simulations followed by estimation were performed to illustrate this work. 
Material and Methods 
Simulation step The data set included 768 data samples from 256 subjects. The time course profile of a drug was simulated by a one-compartment model with first-order absorption. The clearance was assumed to be bimodally distributed in the population : The population total apparent clearance and the interindividual variability were 2.1 L/h and 20 % for the first subpopulation, respectively. For the second subpopulation, three cases were simulated : the population total apparent clearance were 3.5 L/h, 4.2 L/h or 6.3 L/h (ratio clearance subpopulation 1 versus subpopulation 2 equal to 1.5, 2 and 3 respectively) and the interindividual variability was 40 %. For each case, the proportion subpopulation 1 : subpopulation 2 range was 0.1 : 0.9, 0.2 : 0.8, 0.3 : 0.7, 0.4 : 0.6 and 0.5 : 0.5. As a first approach, 100 simulations were performed.
Estimation step The mixture model was implemented during the estimation step. The two estimation methods FO and FOCE with interaction were tested. The bias was calculated for the subpopulations probabilities.
Results 
When using the FO estimation method, the bias was lower than ± 0.02 for the clearance ratio equal to 3 whatever the subpopulations proportion was. For the ratios equal to 1.5 or 2, the more unbalanced the subpopulations proportion was, the larger was the bias. The bias improved faster for the ratio equal to 2 compared to the ratio equal to 1.5 when equilibrating the two subpopulations probabilities ( Table 1 ).
The work is ongoing using the FOCE estimation method. This method was tested for the ratio equal to 1.5 and the subpopulations proportion 0.9 : 0.1. The subpopulations probabilities were well estimated with a bias lower than ± 0.02 ( Table 2 ). 
Table 1 : FO estimation method ( N=100)
Simulation	Subpopulation proportion
(Means) ± SD
Bias			
	Ratio 1.5	Ratio 2	Ratio 3	
0.9 : 0.1	(0.78 : 0.22) ± 0.21
- 0.12 : + 0.12	(0.80 : 0.20) ± 0.16
- 0.10 : + 0.10	(0.88 : 0.12) ± 0.06
- 0.02 : + 0.02	
0.8 : 0.2	(0.70 : 0.30) ± 0.21
- 0.10 : + 0.10	(0.74 : 0.26) ± 0.15
- 0.06 : + 0.06	(0.78 : 0.22) ± 0.07
- 0.02 : + 0.02	
0.7 : 0.3	(0.66 : 0.34) ± 0.20
- 0.04 : + 0.04	(0.65 : 0.35) ± 0.14
- 0.05 : + 0.05	(0.69 : 0.31) ± 0.06
- 0.01 : + 0.01	
0.6 : 0.4	(0.64 : 0.36) ± 0.18
+ 0.04 : - 0.04	(0.59 : 0.41) ± 0.15
- 0.01 : + 0.01	(0.60 : 0.40) ± 0.08
+ 0.006 : - 0.006	
0.5 : 0.5	(0.57 : 0.43) ± 0.18
+ 0.07 : - 0.07	(0.54 : 0.46) ± 0.15
+ 0.04 : - 0.04	(0.52 : 0.48) ± 0.09
+ 0.02 : - 0.02	
Table 2 : FOCE estimation method ( N=93)*
Simulation	Subpopulation proportion
(Means) ± SD
Bias	
	Ratio 1.5	
0.9 : 0.1	(0.90 : 0.10) ± 0.097
- 0.003 : + 0.003	
* : 7 non successful runs
Conclusion 
Whatever the experimental conditions are, the subpopulation probabilities are likely to be well described with the FOCE estimation method. Using the FO estimation method, the accuracy of the probabilities description depends on the subpopulations proportion and the relative typical values of the bimodally distributed pharmacokinetic parameter. 

Grey-box Modelling of Insulin Clamp Study

Christoffer W. Thornøe, Judith L. Jacobsen and Henrik Madsen
Technical University of Denmark & Novo Nordisk A/S
poster
Grey-box PK/PD Modelling of insulin is presented as a promising way of modelling the dynamics of the insulin/glucose system and to estimate model and derived PK/PD parameters. The concept behind grey-box modelling consists of using a priori knowledge, along with information from data in the estimation of model parameters. The PK/PD parameters are estimated simultaneously and used for simula-tion which fits the measured data very well, thereby describing the uptake, delivery and effect of two types of insulin.
The grey-box state space model for the effect compartment is modelled using stochastic differential equations. The parameters are estimated using the Maximum Likelihood method, in which the likehood function is updated using the Kalman Filter. 
Conclusion:
•	The advantage of using grey-box PK/PD models is that the prior physiologic knowledge is combined with the information from the data. 
•	It is possible to assess the correlation between PK and PD parameters because they are estimated simultaneously. 
•	More reliable information about the insulin/glucose system is obtained since all the available data is used in the estimation procedure. 

Pharmacokinetic mixed effects modelling of a new compound in rat - Combined analysis.

D. Martin , N. Frey , C. Laveille , H. Merdjan and R. Jochemsen
Servier Research and Development
poster
Introduction and Objectives Several toxicokinetic (TK) and pharmacokinetic (PK) studies have been performed with a new drug composed of two stable ions, a natural endogenous compound, and an organic moiety. The combination of studies covered a variety of experimental conditions, including a broad range of doses. Pharmacokinetic information from TK studies was often limited to sparse sampling in only a few animals whereas PK studies generally provided more information. All PK and TK data were pooled in a combined population PK analysis, in an attempt to provide an overall description and/or better understanding of the PK properties of the stable ion (XX) in the rat. 
Methods Data description Six studies used in this combined analysis covered a combination of single and multiple oral and single intravenous administration. Due to the difficulty in distinguishing between intra-individual, interindividual and residual variability and because of the increase of animal weight with time, rats with several days of treatment were considered to be different animals. After single intravenous administration, the unit doses of XX ranged from 1.7 to 9.3 mg. After oral administration, the unit doses of XX ranged from 4.6 to 198 mg and the duration of treatment ranged from one day to 26 weeks. The final database consisted of 858 data from 448 (112 male and 336 female) rats 
Model The plasma concentrations were modelled using NONMEM. In each rat, there is a pre-existing endogenous level and this has to be taken into account in the model. The plasma concentration time data were fitted to a series of compartment disposition models, which were parameterised in terms of clearances and volumes of distribution. The absorption process was parameterised in terms of a rate constant and bioavailability (F1). The residual error model was proportional. The first order (FO) method was used to fit the data. 
Results and conclusion The concentration-time data were best described by a four compartment model and significant relationships were found between bioavailability (F1) and Dose, and between endogenous level and gender. Furthermore, statistically significant different Ka and F1 were determined for a particular study, in relation to the age of animals (improved bioavailability in young animals). The rate of absorption was moderate, whatever the dose administered. The population bioavailability of this compound in rats decreased with increasing dose in agreement with the known saturable absorption. This compound is characterised by a very long terminal half-life of at least 80 days. In conclusion, this population model enabled determination of the time and dose effect, as well as identification of the important covariates on XX PK in the rat in the dose range studied during the development of this compound. In addition, it could be used to estimate individual XX PK parameters by bayesian feedback for studies using sparse sampling times in rats. 

The propagation of information in PK modelling: The use of IV information to support the analysis of PK data

In-Sun Nam, Leon Aarons
School of Pharmacy, University of Manchester, UK
poster
A logical method of information transfer from IV to oral data was investigated using four data sets generated from phase I studies which differed in design, study population and sampling scheme. 
Drug in question has fast absorption with nearly complete bioavailability. Its kinetics are linear and show biexponential elimination with a terminal half-life of 7.5 to 9 hours. From the analysis of IV data (Data I, Data III: bioavailability data (IV + ORAL)), it was shown that the drug has a very rapid early distribution (clearance (CL): 20.5 L/hr, distributional clearance (CLD): 171.2 L/hr, volume of compartment one (V1): 17.3 L and volume of compartment two (V2): 166.8 L). 
As the fraction of dose eliminated associated with the first exponential term was less than 10 %, identifying early distribution parameters such as CLD and V1 was not easy in the oral data analysis (Data II). These parameters were correlated with absorption parameters, and even with moderate amounts of data in the early disposition phase (single dose data: SOD), the analysis might produce multiple numerical solutions (based on close simulations). In the case of a multiple oral dose study (MOD) with few data in the early phase, one compartment model was preferred, as the value of V1 approached that of VSS. Moreover, the pooled analysis for SOD and MOD produced results which overestimated V1, underestimated CLD (CL/F: 20.5 L/hr, CLD/F: 54.7 L/hr, V1/F: 67.0 L, V2/F: 151.7 L and Infusion time of 3.0 hr with a zero order model).
Two approaches were taken to resolve this problem; one was a simultaneous approach where IV data were analysed together with SOD/MOD using NLME[2]. While the analysis of all the IV data with SOD produced reasonable results, the analysis of all the available data including MOD generated overestimated V1 as well as underestimated CLD. Moreover, the range of the individual V1 estimates for MOD was different from that for SOD or Data III.
The other approach was a sequential one using the Bayesian program PKBUGS[3]. Here SOD or MOD were analysed separately given appropriate prior knowledge from previous analyses. The analysis of SOD was performed with an informative prior on fixed effects directly from the IV analysis results and a weak prior on random effects, which generated not only an reasonable results, but also the range of individual V1 estimates were much stabilised and the random effects for the absorption parameters were also estimable. Nonetheless, the analysis of MOD required a strong prior on random effects as well; otherwise the variation of individual V1 estimates for MOD allowed the values to be inflated unrealistically (CL/F: 20.1 L/hr, CLD/F: 185.7 L/hr, V1/F: 20.1 L, V2/F: 188.1 L, lag Time: 0.46 hr and Infusion time of 2.2 hr). 
In conclusion, Bayesian approach offers a unique way to incorporate the existing knowledge, which is logical and sensible. Moreover, it provides more stability in terms of estimating random effects with limited data
References:
[1] Pinheiro, J. C. and Bates, D. M. The NLME model formulation, Springer, New York, 2000.
[2] Lunn, D. J., Wakefield, J., Thomas, A., Best, N. and Spiegelhalter, D. PKBUGS User Guide, Epidemiology & public health at Imperial College School of Medicine, London, 1999.

Population pharmacokinetics of high-dose etoposide in children receiving different conditioning regimens

G.Würthwein1, T.Klingebiel2, S.Krümpelmann3,  M.Metz4, K.Schwenker4, C.Lanvers1, J. Boos1
1 University Children´s Hospital Münster, Department of Pediatric Hematology and Oncology, D-48129 Münster. 2 University Hospital Frankfurt, Department of Pediatric Hematology and Oncology, Theodor-Stern-Kai 7, D-60596 Frankfurt. 3 Hospital for Children, Darmstadt, Dieburgerstraße 31, D-64287 Darmstadt, 4 University Children´s Hospital Tübingen, Rümelinstraße 23, D-72070 Tübingen
poster

Objectives: Many conditioning regimens contain high dose (HD) etoposide (Eto). Linearity of pharmacokinetics for Eto from low dose (LD) to HD schedules was observed in adults, there was no difference between the kinetics in adults and children at lower doses. Data on the kinetics in children under HD conditions are, however, limited.
Methods: Based on clinical drug monitoring data, pharmacokinetics after high dose Eto (40 mg/kg i.v. once as 4 h infusion, 1 patient: 20 mg/kg i.v. as 4 h infusion, for 3 consecutive days) were studied in 31 children and young adults (age 0.8-23.7 years, median: 8.0 years) undergoing bone marrow transplantation (BMT) after different conditioning regimens. Blood samples were collected until 97 h after the end of infusion. The population analysis (P-Pharm 1.5) of the first part of data (112 samples/21 patients, well documented) served to establish the pharmacokinetic model. The same data, combined with the second part of data (50 samples/10 patients, “intention to treat”) then served to calculate the final population model. 
Results: Data were best described by a three compartment model with t½  of 0.28 h ± 3.2 %, t½ ß of 3.6 h ± 16.9 % and t½  of 44.2 h ± 56.5 %, respectively (meangeom ± CVgeom). Clearance (CL) was 15.5 ml/min/m2 ± 30.6 % (meangeom ± CVgeom). The fraction of unbound Eto (fu) was 7.0 % (4.3 %  -  11.9 %) (median (range)), with high intra-individual variability. An increase in fu with increasing total Eto was observed. 
Discussion: Most published data on the PK of Eto showed biexponential Eto disappearance. Besides the present drug monitoring there are only few studies reported in literature after high dose Eto that found a third compartment - all these studies showed long times of sample collection after end of infusion. Eto CL was low compared to data reported in the literature. The relatively low Eto CL together with findings of a deep third compartment may not only influence total AUC but also plasma drug concentration at time of BMT. The question of a principally lower Eto CL in children, as compared to adults, after high dose treatment remains open.
Ref.: Würthwein G. et al: Population pharmacokinetics of high-dose etoposide in children receiving different conditioning regimens. Anti-Cancer Drugs: 13: 101-110, 2002